Question

CMR hằng đẳng thức: x^2+2x+11 luôn dương

Answer 1

x²+2x+11=(x²+2x+1)+10=(x+1)²+10

Do (x+1)²>0=>(x+1)²+10>0

=>(x+1)²+10 luôn dương

=>x²+2x+11 luôn dương(đpcm)

Answer 2

x^2+2x+11

=x²+2x+1+10

=(x+1)²+10 >0 với mọi x ( vì (x+1)^2\(>\)0)

vậy  x^2+2x+11 luôn dương

Answer 3

Lê Quang Phúc copy 

Answer 4

\(=\left(x+1\right)^2+10\ge10\)

Vậy bài toán trên luôn dương với mọi x

Answer 5

TA CÓ:\(x^2+2x+11=x^2+2.1.x+1^2+10=\left(x^2+2.1.x+1^2\right)+10=\left(x+1\right)^2+10\)

do:\(\left(x+1\right)^2\ge0\Rightarrow\left(x+1\right)^2+10\ge10>0\left(đpcm\right)\)

Answer 6

\(x^2+2x+11\)

\(=x^2+2.1.x+1+10\)

\(=\left(x^2+2.1.x+1^2\right)+10\)

\(=\left(x+1\right)^2+10\)

do   \(\left(x+1\right)^2\ge0,\)\(10>0\)

\(\Rightarrow\left(x+1\right)^2+10>0\)

\(\Rightarrow\)\(x^2+2x+11\)luôn dương