Question

Rezolvati ecuatia : $\sqrt{x+5}+ \sqrt{x+3}= \sqrt{2x+7}$. Mersi.

Answer 1

[tex]\sqrt{x+5}+\sqrt{x+3}=\sqrt{2x+7}|()^2\\ x+5+2\sqrt{(x+3)(x+5)}+x+3=2x+7\\ 2x+8+2\sqrt{(x+3)(x+5)}=2x+7\\ 2\sqrt{(x+3)(x+5)}=-1 \\ \sqrt{(x+3)(x+5)}=-\frac{1}{2}|()^2\\ (x+3)(x+5)=\frac{1}{4}\\ x^2+3x+5x+15=\frac{1}{4}\\ x^2+8x+15-\frac{1}{4}=0\\ x^2+8x+\frac{59}{4}=0\\ \Delta=64-4\cdot \frac{59}{4}\\ \Delta=64-59\\ \Delta=5 \Rightarrow \sqrt{\Delta}=\sqrt{5}\\ x_1=\frac{-8+\sqrt{5}}{2}\\ x_2=\frac{-8-\sqrt{5}}{2}=-\frac{8+\sqrt{5}}{2}[/tex]