Question

Chứng minh đa thức sau vô nghiệm
a) x^2+19
b) -x^2-2/5
c) (x-1)^2+(x+5)^2
 

Answer 1

\(\text{a},x^2\)≥ 0

\(x^2+19>0\)

=> pt vô no

b, \(-x^2< =0\\ -x^2-\dfrac{2}{5}< 0\)

=> pt vô no

c, \(\left(x-1\right)^2\)≥ 0

\(\left(x+5\right)^2\) ≥ 0

\(\left(x-1\right)^2+\left(x+5\right)^2>0\)

=> pt vô no

Answer 2

a) Ta có: \(x^2\ge0\Rightarrow x^2+19\ge19>0\)

\(\Rightarrow\) Vô nghiệm

b) \(-x^2\le0\Rightarrow-x^2-\dfrac{2}{5}< \dfrac{-2}{5}< 0\)

\(\Rightarrow\) Vô nghiệm

c) \(\left(x-1\right)^2+\left(x+5\right)^2\)

Có: \(\left\{{}\begin{matrix}\left(x-1\right)^2=0\\\left(x+5\right)^2=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)

\(\Rightarrow\) Vô nghiệm