Question

Cho \(x^2-x=4.\) Tính \(M=x^4-2x^3+3x^2-2x+2\)

Answer 1

Ta có: M = \(x^4-2x^3+3x^2-2x+2\)

= \(\left(x^4-x^3\right)-\left(x^3-x^2\right)+\left(2x^2-2x\right)+2\)

= \(x^2\left(x^2-x\right)-x\left(x^2-x\right)+2\left(x^2-x\right)+2\)

= \(\left(x^2-x\right)\left(x^2-x+2\right)+2\) (1)

Thay \(x^2-x=4\) vào (1) ta được:

\(4\left(4+2\right)+2=26\)

Vậy .....................