Question

Chứng minh mỗi biểu thức sau luôn dương

a/ x^2+6x+10

C/x^2-x+1

e/x^4-4x^2+5

giúp hộ e

Answer 1

a) \(x^2+6x+10\)

\(=\left(x^2+2.3x+9\right)+1\)

\(=\left(x+3\right)^2+1\ge1>0\)

\(\Rightarrow DPCM\)

b) \(x^2-x+1\)

\(=\left(x^2-2.\frac{1}{2}x+\frac{1}{4}\right)+\frac{3}{4}\)

\(=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)

\(\Rightarrow DPCM\)

c) \(x^4-4x^2+5\)

\(=\left[\left(x^2\right)^2-2.2.x^2+2^2\right]+1\)

\(=\left(x^2-2\right)^2+1\ge1>0\)

\(\Rightarrow DPCM\)