Question

CM : \(x^4+2012x^2-2011x+2012>0\)

Answer 1

Lời giải:

Ta có:
\(x^4+2012x^2-2011x+2012=x^4+x^2+2011(x^2-x+\frac{1}{4})+\frac{6037}{4}\)

\(=x^4+x^2+2011(x-\frac{1}{2})^2+\frac{6037}{4}\)

Vì \(x^4\geq 0,x^2\geq 0, (x-\frac{1}{2})^2\geq 0, \forall x\)

\(\Rightarrow x^4+x^2+2011(x-\frac{1}{2})^2+\frac{6037}{4}\geq \frac{6037}{4}>0\) với mọi $x$

Ta có đpcm.