Question

Chứng minh rằng:

\(P=x^4-2x^3+2x^2-2x+1\text{ ≥}0\) với mọi giá trị x

Answer 1

P = \(x^4-2x^3+2x^2-2x+1\)

P = \(x^4-x^3-x^3+x^2+x^2-x-x+1\)

P = \(x^3\left(x-1\right)-x^2\left(x-1\right)+x\left(x-1\right)-\left(x-1\right)\)

P = \(\left(x-1\right)\left(x^3-x^2+x-1\right)\)

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

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

P = \(\left(x-1\right)^2\left(x^2+1\right)\) \(\ge\forall x\) ( đpcm )

Chúc bạn học tốt :))