Question

Cho đa thức:

A= 2x²+|7x-1|-(5-x+2x²)

a, Thu gọn A

Tìm x để A=2

Answer 1

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

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

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

\(\Rightarrow\left[{}\begin{matrix}A=7x-1-5+x\left(đk:x\ge\dfrac{1}{7}\right)\\A=-7x+1-5+x\left(đk:x< \dfrac{1}{7}\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}A=8x-6\\A=-6x-4\end{matrix}\right.\)

Để A =2 thì ta có:

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

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

\(\Rightarrow\left[{}\begin{matrix}7x-1=7-x\left(đk:x\ge\dfrac{1}{7}\right)\\-7x+1=7-x\left(đk:x< \dfrac{1}{7}\right)\end{matrix}\right.\)

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