Question

chứng minh biểu thức luôn âm với Aa)-9x²+12-15b)-10-(x-1)(x+2)c)-x²+x-2

Answer 1

a) sai đề sửu lại

\(-9x^2+12x-15=-\left(9x^2-12x+4\right)-11=-\left(3x-2\right)^2-11\)

Vì: \(-\left(3x-2\right)^2\le0\)

=> \(-\left(3x-2\right)^2-11< 0\)

=>đpcm

b) \(-10-\left(x-1\right)\left(x+2\right)=-10-x^2-2x+x+2=-\left(x^2+x+\frac{1}{4}\right)-\frac{31}{4}=-\left(x+\frac{1}{2}\right)^2-\frac{31}{4}\)

Vì: \(-\left(x+\frac{1}{2}\right)^2\le0\)

=> \(-\left(x+\frac{1}{2}\right)^2-\frac{31}{4}< 0\)

=>đpcm

c) \(-x^2+x-2=-\left(x^2-x+\frac{1}{4}\right)-\frac{7}{4}=-\left(x-\frac{1}{2}\right)^2-\frac{7}{4}\)

Vì: \(-\left(x-\frac{1}{2}\right)^2\le0\)

=> \(-\left(x-\frac{1}{2}\right)^2-\frac{7}{4}< 0\)

=>đpcm