Hướng dẫn Giải Bài 2 (Trang 133, SGK Toán Giải tích 12)

Hướng dẫn giải Bài 2 (Trang 133 SGK Toán Giải tích 12)

Bài 2 (Trang 133 SGK Toán Giải tích 12): Tìm các số thực x và y biết: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mo>)</mo><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><mn>2</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mi mathvariant="normal">i</mi><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">y</mi><mo> </mo><mo>-</mo><mo> </mo><mn>5</mn><mo>)</mo><mi mathvariant="normal">i</mi></math>  ; b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi></mrow></mfenced><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">i</mi><msqrt><mn>3</mn></msqrt><mo> </mo><mo>=</mo><mo> </mo><msqrt><mn>5</mn></msqrt><mo> </mo><mo>+</mo><mo> </mo><mfenced><mrow><mn>1</mn><mo> </mo><mo>-</mo><mo> </mo><mn>3</mn><mi mathvariant="normal">y</mi></mrow></mfenced><mi mathvariant="normal">i</mi></math>  ; c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">y</mi></mrow></mfenced><mo> </mo><mo>+</mo><mo> </mo><mfenced><mrow><mn>2</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>-</mo><mo> </mo><mi mathvariant="normal">x</mi></mrow></mfenced><mi mathvariant="normal">i</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced><mrow><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn></mrow></mfenced><mo> </mo><mo>+</mo><mo> </mo><mfenced><mrow><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></mrow></mfenced><mi mathvariant="normal">i</mi></math>. Hướng dẫn giải: Áp dụng a+ bi = c + di <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">a</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">c</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">d</mi></mtd></mtr></mtable></mfenced></math> a) <math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="18px"><mo>(</mo><mn>3</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><mn>2</mn><mi mathvariant="normal">y</mi><mo>+</mo><mn>1</mn><mo>)</mo><mi mathvariant="normal">i</mi><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo> </mo><mo>-</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">y</mi><mo>-</mo><mn>5</mn><mo>)</mo><mi mathvariant="normal">i</mi><mo> </mo><mo>⇔</mo><mfenced open="{" close=""><mtable columnspacing="1.4ex" columnalign="left"><mtr><mtd><mn>3</mn><mi mathvariant="normal">x</mi><mo>-</mo><mn>2</mn><mo>=</mo></mtd><mtd><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mn>1</mn><mo> </mo><mo>=</mo></mtd><mtd><mo>-</mo><mo>(</mo><mi mathvariant="normal">y</mi><mo>-</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></mstyle></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo mathsize="18px">(</mo><mn mathsize="18px">1</mn><mo mathsize="18px">-</mo><mn mathsize="18px">2</mn><mi mathvariant="normal" mathsize="18px">x</mi><mo mathsize="18px">)</mo><mo mathsize="18px"> </mo><mo mathsize="18px">-</mo><mo mathsize="18px"> </mo><mi mathvariant="normal" mathsize="18px">i</mi><msqrt><mn mathsize="18px">3</mn></msqrt><mo mathsize="18px"> </mo><mo mathsize="18px">=</mo><mo mathsize="18px"> </mo><msqrt><mn mathsize="18px">5</mn></msqrt><mo mathsize="18px"> </mo><mo mathsize="18px">+</mo><mo mathsize="18px"> </mo><mo mathsize="18px">(</mo><mn mathsize="18px">1</mn><mo mathsize="18px">-</mo><mn mathsize="18px">3</mn><mi mathvariant="normal" mathsize="18px">y</mi><mo mathsize="18px">)</mo><mi mathvariant="normal" mathsize="18px">i</mi><mo mathsize="18px"> </mo><mo mathsize="18px">⇔</mo><mstyle mathsize="18px"><mo>{</mo><mtable columnspacing="1.4ex" columnalign="left"><mtr><mtd><mn>1</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">x</mi><mo>=</mo></mtd><mtd><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mn>1</mn><mo>-</mo><mn>3</mn><mi mathvariant="normal">y</mi><mo>=</mo></mtd><mtd><mo>-</mo><msqrt><mn>3</mn></msqrt></mtd></mtr></mtable></mstyle><mo mathsize="18px">⇔</mo><mstyle mathsize="18px"><mo>{</mo><mtable columnspacing="1.4ex" columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo>=</mo></mtd><mtd><mstyle displaystyle="false"><mfrac><mrow><mn>1</mn><mo>-</mo><msqrt><mn>5</mn></msqrt></mrow><mn>2</mn></mfrac></mstyle></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo>=</mo></mtd><mtd><mstyle displaystyle="false"><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac></mstyle></mtd></mtr></mtable></mstyle></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo mathsize="18px">(</mo><mn mathsize="18px">2</mn><mi mathvariant="normal" mathsize="18px">x</mi><mo mathsize="18px">+</mo><mi mathvariant="normal" mathsize="18px">y</mi><mo mathsize="18px">)</mo><mo mathsize="18px"> </mo><mo mathsize="18px">+</mo><mo mathsize="18px"> </mo><mo mathsize="18px">(</mo><mn mathsize="18px">2</mn><mi mathvariant="normal" mathsize="18px">y</mi><mo mathsize="18px">-</mo><mi mathvariant="normal" mathsize="18px">x</mi><mo mathsize="18px">)</mo><mi mathvariant="normal" mathsize="18px">i</mi><mo mathsize="18px"> </mo><mo mathsize="18px">=</mo><mo mathsize="18px"> </mo><mo mathsize="18px">(</mo><mi mathvariant="normal" mathsize="18px">x</mi><mo mathsize="18px">-</mo><mn mathsize="18px">2</mn><mi mathvariant="normal" mathsize="18px">y</mi><mo mathsize="18px">+</mo><mn mathsize="18px">3</mn><mo mathsize="18px">)</mo><mo mathsize="18px"> </mo><mo mathsize="18px">+</mo><mo mathsize="18px"> </mo><mo mathsize="18px">(</mo><mi mathvariant="normal" mathsize="18px">y</mi><mo mathsize="18px">+</mo><mn mathsize="18px">2</mn><mi mathvariant="normal" mathsize="18px">x</mi><mo mathsize="18px">+</mo><mn mathsize="18px">1</mn><mo mathsize="18px">)</mo><mi mathvariant="normal" mathsize="18px">i</mi><mo mathsize="18px"> </mo><mo mathsize="18px">⇔</mo><mstyle mathsize="18px"><mo>{</mo><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mi mathvariant="normal">x</mi><mo>-</mo><mn>2</mn><mi mathvariant="normal">y</mi><mo>+</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi mathvariant="normal">y</mi><mo>-</mo><mi mathvariant="normal">x</mi><mo>=</mo><mi mathvariant="normal">y</mi><mo>+</mo><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo>+</mo><mn>3</mn><mi mathvariant="normal">y</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></mstyle><mspace linebreak="newline"/></math>