\(-x^2+x-\dfrac{1}{2}\)
\(=-\left(x^2-x+\dfrac{1}{2}\right)\)
\(=-\left(x^2-x+\dfrac{1}{4}+\dfrac{1}{4}\right)\)
\(=-\left(x-\dfrac{1}{2}\right)^2-\dfrac{1}{4}< 0\)
CMR:
\(-\dfrac{1}{2}-x^2+x< 0\) ∀ \(x\)
CMR: \(x-x^2-1< 0\forall x\)
CMR \(x^2-5xy+z^2+10y^2+2>0\forall x,y,z\)
CMR
\(-4+5-x^2< 0\forall x\)
Tìm
Min Q=\(\dfrac{x^2-3x+3}{\left(x-1\right)^2}\forall x\ne1\)
Chứng minh: \(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2}+4\ge3\left(\dfrac{x}{y}+\dfrac{y}{x}\right)\) luôn đúng với \(\forall x,y\ne0\)
Tìm
Min Q = \(\dfrac{x^2-3x+3}{\left(x-1\right)^2}\) ∀ \(x\ne1\)
Chứng minh: x2-x+1 >0 \(\forall\)x
CMR A= x\(^4\) - 12x\(^3\) + 46x\(^2\) - 60x + 25 \(\ge\) 0, \(\forall\)x
