Question

4x^4+5x^2+5 lớn hơn 0 với mọi x

Answer 1

\(4x^4+5x^2+5=\left(2x^2\right)^2+2.2x^2.\dfrac{5}{4}+\dfrac{25}{16}+\dfrac{55}{16}=\left(2x^2+\dfrac{5}{4}\right)^2+\dfrac{55}{16}\ge\dfrac{55}{16}>0\)

Answer 2

Ta có: \(4x^4\ge0\forall x\)

\(5x^2\ge0\forall x\)

Do đó: \(4x^4+5x^2\ge0\forall x\)

\(\Leftrightarrow4x^4+5x^2+5>0\forall x\)