Giải bài 13 trang 40 SGK Toán 8 tập 2

Bài tập số 13 trang 40 SGK Toán 8 tập 2 thuộc giải toán 9 tập 2

Đề bài

a) <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a+5" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a+5a+5 < <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="b+5" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">b+5b+5 b) <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−3a&gt;−3b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−3a>−3b−3a>−3b;

c) <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a−6≥5b−6" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a−6≥5b−65a−6≥5b−6;

d) <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a+3≤−2b+3" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a+3≤−2b+3−2a+3≤−2b+3.

Phương pháp và lời giải chi tiết

a) Ta có: <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a+5&lt;b+5" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a+5<b+5a+5<b+5

Cộng <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="(−5)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">(−5)(−5) và hai vế bất đẳng thức <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a+5&lt;b+5" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a+5<b+5a+5<b+5 ta được:

<span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a+5+(−5)&lt;b+5+(−5)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a+5+(−5)<b+5+(−5)a+5+(−5)<b+5+(−5)

Do đó: <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a&lt;b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a<ba<b. b) Ta có: <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−3a&gt;−3b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−3a>−3b−3a>−3b

Nhân cả hai vế bất đẳng thức <span id="MathJax-Element-12-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−3a&gt;−3b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−3a>−3b−3a>−3b với <span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−13&lt;0" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−13<0−13<0 ta được:

<span id="MathJax-Element-14-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−3a.(−13)&lt;−3b.(−13)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−3a.(−13)<−3b.(−13)−3a.(−13)<−3b.(−13)

Do đó: <span id="MathJax-Element-15-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a&lt;b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a<ba<b c) Ta có: <span id="MathJax-Element-16-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a−6≥5b–6" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a−6≥5b–65a−6≥5b–6 Cộng hai vế bất đẳng thức <span id="MathJax-Element-17-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a−6≥5b−6" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a−6≥5b−65a−6≥5b−6 với <span id="MathJax-Element-18-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="6" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">66 ta được: <span id="MathJax-Element-19-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a−6+6≥5b−6+6" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a−6+6≥5b−6+65a−6+6≥5b−6+6 Do đó: <span id="MathJax-Element-20-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a≥5b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a≥5b5a≥5b Nhân hai vế bất đẳng thức <span id="MathJax-Element-21-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a≥5b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a≥5b5a≥5b với <span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="15&gt;0" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">15>015>0 ta được:

<span id="MathJax-Element-23-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="5a.15⩾5b.15" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">5a.15⩾5b.155a.15⩾5b.15

Do đó: <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a≥b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a≥ba≥b

d) <span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a+3≤−2b+3" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a+3≤−2b+3−2a+3≤−2b+3

Cộng hai vế bất đẳng thức <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a+3≤−2b+3" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a+3≤−2b+3−2a+3≤−2b+3 với <span id="MathJax-Element-27-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="(−3)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">(−3)(−3) ta được

<span id="MathJax-Element-28-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a+3+(−3)≤−2b+3+(−3)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a+3+(−3)≤−2b+3+(−3)−2a+3+(−3)≤−2b+3+(−3)

Do đó: <span id="MathJax-Element-29-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a≤−2b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a≤−2b−2a≤−2b

Nhân cả hai vế bất đẳng thức <span id="MathJax-Element-30-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a≤−2b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a≤−2b−2a≤−2b với <span id="MathJax-Element-31-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−12&lt;0" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−12<0−12<0 ta được:

<span id="MathJax-Element-32-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="−2a(−12)⩾−2b.(−12)" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">−2a(−12)⩾−2b.(−12)−2a(−12)⩾−2b.(−12)

Do đó <span id="MathJax-Element-33-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="a≥b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 18.45px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">a≥b