Question

cho x²+2x-2=0 tinh gia tri bieu thuc M=x⁴+16x+2007

Answer 1

\(x^2+2x-2=0\Rightarrow\left\{{}\begin{matrix}x^2+2x+1=3\\x^2=2-2x\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left(x+1\right)^2=3\\x^4=4x^2-8x+4\end{matrix}\right.\)

Thay vào biểu thức:

\(M=x^4+16x+2007=4x^2-8x+4+16x+2007\)

\(\Rightarrow M=4x^4+8x+4+2007=4\left(x+1\right)^2+2007=4.3+2007=2019\)

Answer 2

M = (x⁴ + 2x³ - 2x²) - (2x³ + 4x² - 4x) + (6x² + 12x - 12) + 2019

M = x²(x² + 2x - 2) - 2x(x² + 2x - 2) + 6(x² + 2x - 2) + 2019

M = 0 + 0 + 0 + 2019

M = 2019