Question

chứng minh rằng  2x²+4x+3>0 với mọi x

Answer 1

2x^2+4x+2+1>0

2(x+1)^2+1>0 (đúng) 

suy ra đpcm 

Answer 2

\(2x^2+4x+3\)

\(=2\left(x^2+2x+\frac{3}{2}\right)\)

\(=2\left(x^2+2x+1^2-1^2+\frac{3}{2}\right)\)

\(=2\left[\left(x+1\right)^2+\frac{1}{2}\right]\)

\(=2\left(x+1\right)^2+1>0\forall x\)