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Giải bài 8 trang 16 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Cho phương trình x2 + 6x – 91 = 0. Gọi x1, x2 là hai nghiệm của phương trình. Khi đó, giá trị của biểu thức (x_1^2 + x_2^2 - 2{x_1} - 2{x_2}) là A. 127 B. 230 C. – 230 D. – 127

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Cho phương trình x2 + 6x – 91 = 0. Gọi x1, x2 là hai nghiệm của phương trình. Khi đó, giá trị c𒅌ủa biểu thức \(x_1^2 + x_2^2 - 2{x_1} - 2{x_2}\) là

A. 127

B. 230

C. – 230

D. – 127

Phương pháp giải - Xem chi tiết

Dựa vào: Nếu phương trình bậc hai ax2 + bx + c = 0 (a\( \ne \)0) có nghiệm x1, x2 thì tổng và tích của hai nghiệm đó là:

\(S = {x_1} + {x_2} =  - \frac{b}{a};P = {x_1}.{x_2} = \frac{c}{a}\)

Lời giải chi tiết

Phương trình x2 + 6x – 91 = 0 có a = 1 và c = - 91 trái dấu nên có hai nghiệm phân biệt x1; x2.

Theo định lí Viète, ta có: \(S ={x_1} + {x_2} =  - \frac{b}{a} =  - 6;P = {x_1}{x_2} = \frac{c}{a} =  - 91\). Ta có: \(\begin{array}{l}x_1^2 + x_2^2 - 2{x_1} - 2{x_2} \\= {\left( {{x_1} + {x_2}} \right)^2} - 2{x_1}{x_2} - 2({x_1} + {x_2})\\ = {S^2} - 2P - 2S\\ = {( - 6)^2} - 2.( - 91) - 2.( - 6) \\= 230\end{array}\) Chọn đáp án B.

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