Giải bài 5 trang 7 SGK Toán 8 tập 2

Giải bài 5 trang 7 SGK Toán 8 tập 2: Hai phương trình x = 0 và x(x - 1) = 0 có tương đương không? Vì sao?

Bài tập số 5 trang 7 SGK Toán 8 tập 2 thuộc chương III của phương trình bậc nhất một ẩn và là Bài 1: Mở đầu về phương trình

xem thêm: Giải Toán 8

Đề bài

<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x=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;">x=0x=0 và <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x(x−1)=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;">x(x−1)=0x(x−1)=0

Phương pháp và lời giải chi tiết

Phương trình <span id="MathJax-Element-3-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x=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;">x=0x=0 có tập nghiệm <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="S1={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;">S1={0}S1={0}.

Xét phương trình <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x(x−1)=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;">x(x−1)=0x(x−1)=0.

Ta có một tích bằng <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="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;">00 khi một trong hai thừa số bằng <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="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;">00 tức là:

<span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x(x−1)=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;">x(x−1)=0x(x−1)=0 khi <span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x=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;">x=0x=0 hoặc <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x=1" 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;">x=1x=1.

Vậy phương trình <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="x(x−1)=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;">x(x−1)=0x(x−1)=0 có tập nghiệm <span id="MathJax-Element-12-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="S2={0;1}" 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;">S2={0;1}S2={0;1}

Vì <span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="S1≠S2" 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;">S1≠S2S1≠S2 nên hai phương trình không tương đương.