Question

Giúp mình với :

\(\dfrac{1}{2x+2+5\sqrt{x}}+\dfrac{1}{2\sqrt{x^2+4x+1}+\sqrt{x}}\)

Chứng minh nó khác 0 với ≥0

Answer 1

Do \(x\ge0\Rightarrow2x+2+5\sqrt{x}\ge0+2+0=2>0\Rightarrow\dfrac{1}{2x+2+5\sqrt{x}}>0\)

\(2\sqrt{x^2+4x+1}+\sqrt{x}\ge2\sqrt{0+4.0+1}+0=2>0\Rightarrow\dfrac{1}{2\sqrt{x^2+4x+1}+\sqrt{x}}>0\)

\(\Rightarrow\dfrac{1}{2x+2+5\sqrt{x}}+\dfrac{1}{2\sqrt{x^2+4x+1}+\sqrt{x}}>0\)