Question

Chứng minh

a,x^2+4x+10>0                                         b,x^2-6x+15>0

c,-x^2+2x-5<0

Answer 1

a) \(x^2+4x+10\)

\(=x^2+4x+4+6\)

\(=\left(x+2\right)^2+6\)

Mà: \(\left(x+2\right)^2+6>0\forall x\)

\(\Rightarrow x^2+4x+10>0\forall x\)

b) \(x^2-6x+15\)

\(=x^2-6x+9+6\)

\(=\left(x-3\right)^2+6\)

Mà: \(\left(x-3\right)^2+6>0\forall x\)

\(\Rightarrow x^2-6x+16>0\forall x\)

c) \(-x^2+2x-5\)

\(=-\left(x^2-2x+5\right)\)

\(=-\left(x^2-2x+1+4\right)\)

\(=-\left(x-1\right)^2-4\)

Mà: \(-\left(x-1\right)^2-4< 0\forall x\)

\(\Rightarrow-x^2+2x-5< 0\forall x\)