Question

[Diệu Anh]

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

Rút gọn

\(7\sqrt{a}-5b\sqrt{16a^3}+4a\sqrt{25ab^2}-3\sqrt{16a}\) với a>0, b>0

Answer 1

[An Thy]

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

Vì \(VT\ge2\Rightarrow VP\ge2\Rightarrow x\ge\dfrac{2}{3}\)

\(\Rightarrow\sqrt{\left(2x-1\right)^2}+2=3x\Rightarrow\left|2x-1\right|+2=3x\)

\(\Rightarrow2x-1+2=3x\left(x\ge\dfrac{2}{3}\right)\Rightarrow x=1\)

\(7\sqrt{a}-5b\sqrt{16a^3}+4a\sqrt{25ab^2}-3\sqrt{16a}\)

\(=7\sqrt{a}-20ab\sqrt{a}+20ab\sqrt{a}-12\sqrt{a}=-5\sqrt{a}\)