Question

[☂ℍíρ♧_《Bé Cá Heo 🐋》_ [ Funny 🤣 ]]

CM các đa thức sau vô nghiệm :

G(x) = x^2 + 2x + 3

A(x) = x^2 - x + 1

Answer 1

[Hân.]

\(G\left(x\right)=x^2+2x+3\) 

 \(=x^2+x+x+1+2\)

\(=x.\left(x+1\right)+\left(x+1\right)+2\)

\(=\left(x+1\right).\left(x+1\right)+2\)

\(=\left(x+1\right)^2+2\ge2\)

Vậy G(x) vô nghiệm

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

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

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

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

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

Vậy A(x) vô nghiệm