Question

Va rog, ajutati-ma! Problema pentru clasa 10
rezolvati ecuatiile:

1. $\sqrt{ x^{2} +8} + \sqrt{ x^{2} +3} =5$

2. $\sqrt{2x-1} + \sqrt{2-x} =2$

Answer 1

$\sqrt{x^2+8} =5- \sqrt{x^2+3} => \sqrt{x^2+8}^{2} =(5- \sqrt{x^2+3})^2$
$x^2+8=25+x^2+3-10 \sqrt{x^2+3} =>-20=-10\sqrt{x^2+3} =>$
$2= \sqrt{x^2+3} =>2^2=\sqrt{x^2+3}^2=>4=x^2+3=>x^2=1 =>$
x=+1 sau -1

la fel faci si la 2.