Question

determinați x€R, știind ca (2x-3)²=3

Answer 1

$\displaystyle (2x-3)^2=3 \\ \\ (2x-3)^2-3=0 \\ \\ (2x-3+\sqrt3)(2x-3-\sqrt3)=0 \\ \\ 2x-3+\sqrt3=0 \\ \\ 2x=3-\sqrt3 \\ \\ x=\frac{3-\sqrt3}{2} \\ \\ 2x-3-\sqrt3=0 \\ \\ \sqrt3+3=2x \\ \\ x=\frac{\sqrt3+3}{2} \\ \\ S=\{\pm \frac{\sqrt3+3}{2}\}$