Hướng dẫn giải Bài 3 (Trang 58 SGK Toán Đại số & Giải tích 11)

Biết hệ số của <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup></math> trong khai triển của <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>3</mn><mi>x</mi></mrow></mfenced><mi>n</mi></msup></math> là 90, tìm n Giải Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mn>3</mn><mi>x</mi></mrow></mfenced><mi>n</mi></msup><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msubsup><mo largeop="true">C</mo><mi>n</mi><mi>k</mi></msubsup><mo>.</mo><msup><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mi>k</mi></msup><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msubsup><mo largeop="true">C</mo><mi>n</mi><mi>k</mi></msubsup><mo>.</mo><msup><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mi>k</mi></msup><mo>.</mo><msup><mi>x</mi><mi>k</mi></msup><mspace linebreak="newline"/><mi>H</mi><mi>ệ</mi><mo> </mo><mi>s</mi><mi>ố</mi><mo> </mo><mi>c</mi><mi>ủ</mi><mi>a</mi><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>t</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>k</mi><mi>h</mi><mi>a</mi><mi>i</mi><mo> </mo><mi>t</mi><mi>r</mi><mi>i</mi><mi>ể</mi><mi>n</mi><mo> </mo><mi>l</mi><mi>à</mi><mo> </mo><mspace linebreak="newline"/><msubsup><mo largeop="true">C</mo><mi>n</mi><mn>2</mn></msubsup><msup><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>90</mn><mo>⇔</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>!</mo></mrow></mfrac><mo>=</mo><mn>10</mn><mo>⇔</mo><mi>n</mi><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>20</mn><mo>⇔</mo><mi>n</mi><mo>=</mo><mn>5</mn></math>