Hướng dẫn giải Bài 9 (Trang 107 SGK Toán Đại số & Giải tích 11)

Tìm số hạng đầu <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub></math> và công bội q của các cấp số nhân <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>u</mi><mi>n</mi></msub></mfenced></math>, biết: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>6</mn></msub><mo>=</mo><mn>192</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>7</mn></msub><mo>=</mo><mn>384</mn><mo> </mo><mo>;</mo><mo> </mo></mtd></mtr></mtable></mfenced></math>                                    b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>4</mn></msub><mo>-</mo><msub><mi>u</mi><mn>2</mn></msub><mo>=</mo><mn>72</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>5</mn></msub><mo>-</mo><msub><mi>u</mi><mn>3</mn></msub><mo>=</mo><mn>144</mn><mo> </mo><mo>;</mo><mo> </mo></mtd></mtr></mtable></mfenced></math> c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>2</mn></msub><mo>+</mo><msub><mi>u</mi><mn>5</mn></msub><mo>-</mo><msub><mi>u</mi><mn>4</mn></msub><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>3</mn></msub><mo>+</mo><msub><mi>u</mi><mn>6</mn></msub><mo>-</mo><msub><mi>u</mi><mn>5</mn></msub><mo>=</mo><mn>20</mn><mo>.</mo></mtd></mtr></mtable></mfenced></math> Giải Áp dụng <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mi>n</mi></msub><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></msup></math> a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>6</mn></msub><mo>=</mo><mn>192</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>7</mn></msub><mo>=</mo><mn>384</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>5</mn></msup><mo>=</mo><mn>192</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>6</mn></msup><mo>=</mo><mn>384</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>q</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>4</mn></msub><mo>-</mo><msub><mi>u</mi><mn>2</mn></msub><mo>=</mo><mn>72</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>5</mn></msub><mo>-</mo><msub><mi>u</mi><mn>3</mn></msub><mo>=</mo><mn>144</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>3</mn></msup><mo>-</mo><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><mi>q</mi><mo>=</mo><mn>72</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>4</mn></msup><mo>-</mo><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>2</mn></msup><mo>=</mo><mn>144</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><mi>q</mi><mfenced><mrow><msup><mi>q</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>72</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>(</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mo>.</mo><msup><mi>q</mi><mn>2</mn></msup><mfenced><mrow><msup><mi>q</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>144</mn><mo> </mo><mo> </mo><mo>(</mo><mn>2</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></math> Chia (2) cho (1), ta có q = 2, thay q = 2 vào (1) ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>12</mn></math>. c) Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>2</mn></msub><mo>+</mo><msub><mi>u</mi><mn>5</mn></msub><mo>-</mo><msub><mi>u</mi><mn>4</mn></msub><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>3</mn></msub><mo>+</mo><msub><mi>u</mi><mn>6</mn></msub><mo>-</mo><msub><mi>u</mi><mn>5</mn></msub><mo>=</mo><mn>20</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mi>q</mi><mo>+</mo><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>4</mn></msup><mo>-</mo><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>3</mn></msup><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>2</mn></msup><mo>+</mo><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>5</mn></msup><mo>-</mo><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>4</mn></msup><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math>                                             <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><mi>q</mi><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>q</mi><mn>3</mn></msup><mo>-</mo><msup><mi>q</mi><mn>2</mn></msup></mrow></mfenced><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub><msup><mi>q</mi><mn>2</mn></msup><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>q</mi><mn>3</mn></msup><mo>-</mo><msup><mi>q</mi><mn>2</mn></msup></mrow></mfenced><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced></math> Chia (2) cho (1), ta được q = 2, thay q = 2 vào (1) ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn></math>.

Hướng dẫn Giải Bài 9ab (trang 107, SGK Toán Đại số & Giải Tích 11)

GV:

GV colearn

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