Question

1, tìm x biết 

\(x^2.\left(x-3\right)-4x+12=0\)\(\)

2. chứng minh

\(x-1-x^2< 0\)với mọi số thực x

ai giỏi toán 8 đâu hộ tớ cái ! <3 

ai nhanh nhất tick 3 lần nhé 

Answer 1

Bài 1 :

\(x^2\left(x-3\right)-4x+12=0\)

\(x^2\left(x-3\right)-4\left(x-3\right)=0\)

\(\left(x-3\right)\left(x^2-4\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\x^2-4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=\left\{\pm2\right\}\end{cases}}}\)

Bài 2 :

\(x-1-x^2\)

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

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

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

Vì \(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge0\forall x\)

\(\Rightarrow-\left[\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right]\le0\forall x\left(đpcm\right)\)