Question

Cho biểu thức :

A=x^2+5x+8

Cm A>0 với mọi x

Answer 1

\(A=x^2+5x+8\)

\(=\left(x^2+2.2,5.x+6,25\right)+1,75\)

\(=\left(x+2,5\right)^2+1,75\)

\(\Rightarrow\left(x+2,5\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+2,5\right)^2+1,75\ge1,75\forall x\)

\(\Rightarrow A\ge0\forall x\)

Answer 2

\(A=x^2+5x+8\\ =x^2+5x+6,25+1,75\\ =\left(x+2,5\right)^2+1,75\\ \left(x+2,5\right)^2\ge0\forall x\\ \left(x+2,5\right)^2+1,75\ge1,75\forall x\\ \Rightarrow\left(x+2,5\right)^2+1,75>0\forall x\)