Question

[Đàm Vân Anh]

Cho x^3-x^2-x-2=0. Tính giá trị của biểu thức B=x^9-8x^3+16x^2-2x+2012.

Answer 1

[Lê Anh Tú]

\(x^3-x^2-x-2=0\)

\(\Leftrightarrow x^3-2x^2+x^2-2x+x-2=0\Rightarrow\left(x-2\right).\left(x^2+x+1\right)=0\)

\(x^2+x+1=x^2+2\cdot\frac{1}{2}\cdot x+\frac{1}{4}+\frac{3}{4}=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)

\(x^2+x+1\ne0\Rightarrow x-2=0\Rightarrow x=2\)

\(x^9-8x^3+16x^2-2x+2012\)

\(2^9-8\cdot2^3+16\cdot2^2-2\cdot2+2012=2520\)

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