\(x^4-5x^3+11x^2-12x+6\)
\(=x^4-2x^3+2x^2-3x^3+6x^2-6x+3x^2-6x+6\)
\(=x^2\left(x^2-2x+2\right)-3x\left(x^2-2x+2\right)+3\left(x^2-2x+2\right)\)
\(=\left(x^2-3x+3\right)\left(x^2-2x+2\right)\)
\(=\left(x^2-2x+1+1\right)\left(x^2-3x+\frac{9}{4}+\frac{3}{4}\right)\)
\(=\left(\left(x-1\right)^2+1\right)\left(\left(x-\frac{3}{4}\right)^2+\frac{3}{4}\right)\)
Dễ thấy: \(\left(x-1\right)^2+1>0;\left(x-\frac{3}{4}\right)^2+\frac{3}{4}>0\)
Suy ra ta có ĐPCM
Đúng 0
Bình luận (0)
