Question

Determinați x € R pentru care (3x-4)^2=(2x+1)^2
DAU COROANA!!!!!!!!
ESTE URGENT!!!!!!!!

Answer 1

[tex](3x-4)^2=(2x+1)^2\\ 9x^2-24x+16=4x^2+4x+1\\ 5x^2-28x+15=0\\ \Delta=784-4\cdot 5\cdot 15=484\Rightarrow \sqrt{\Delta}=22\\ x_1=\dfrac{28+22}{10}=\dfrac{50}{10}=5\\ x_2=\dfrac{28-22}{10}=\dfrac{6}{10}=\dfrac{3}{5}\\ \boxed{S:x\in \left \{5, \dfrac{3}{5}\right\}}[/tex]