Question

Cho A= 2x²+/ 7x-1 /- (5-x+ 2x²)

a>Thu gọn A

b)Tìm x để A=2

Answer 1

a) Ta có:

\(A=2x^2+\left|7x-1\right|-\left(5-x+2x^2\right)\)

\(=2x^2+7x-1-5+x-2x^2\)

\(=\left(7x+x\right)-1-5\)

\(=8x-6\)

b) Lại có: \(2x^2+\left|7x-1\right|-\left(5-x+2x^2\right)=2\)

\(\Rightarrow2x^2+\left|7x-1\right|-5+x-2x^2=2\)

\(\Rightarrow\left|7x-1\right|+x=7\)

\(\Rightarrow\left|7x-1\right|=7-x\)

+) TH₁: \(7x-1\ge0\Rightarrow7x\ge1\Rightarrow x\ge\dfrac{1}{7}\)

Khi đó: \(7x-1=7-x\)

\(\Rightarrow7x+x=1+7\)

\(\Rightarrow8x=8\Rightarrow x=1\) (tm)

+) TH₂: \(7x-1< 0\Rightarrow7x< 1\Rightarrow x< \dfrac{1}{7}\)

Lúc đó: \(-7x+1=7-x\)

\(\Rightarrow-7x+x=-1+7\)

\(\Rightarrow-6x=6\Rightarrow x=-1\) (tm)

Vậy \(\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\).