Question

Giải phương trình:

\(4x^2-\left(2+\sqrt{3}\right)^2=0\)

Answer 1

\(4x^2-\left(2+\sqrt{3}\right)^2=0\Leftrightarrow4x^2-\left(2^2+4\sqrt{3}+3\right)=0\Leftrightarrow4x^2-4-4\sqrt{3}-3=0\Leftrightarrow4x^2=7+4\sqrt{3}\Leftrightarrow x^2=\frac{7}{4}+\sqrt{3}\Leftrightarrow x=+,-\sqrt{\frac{7}{4}+\sqrt{3}}\)

Answer 2

\(4x^2-\left(2+\sqrt{3}\right)^2=0\)

\(\Leftrightarrow\left(2x\right)^2=\left(2+\sqrt{3}\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=2+\sqrt{3}\\2x=-2-\sqrt{3}\end{matrix}\right.\)

\(\Leftrightarrow x=\pm\frac{2+\sqrt{3}}{2}\)