Question

rezolvati ecuatia$\sqrt{x^2-x-2$=x-2

Answer 1

   

$\displaystyle\\\sqrt{x^2-x-2}=x-2~~~~~~~\text{(Ridicam la puterea a 2-a)}\\\\ \Big(\sqrt{x^2-x-2}\Big)^2=\Big(x-2\Big)^2\\\\x^2-x-2=x^2-4x+4~~~~~~~\text{(Trecem toti termenii in stanga)}\\\\\underline{x^2}-x-2-\underline{x^2}+4x-4=0\\\\3x-6=0\\\\3x=6\\\\x=\frac{6}{3} \\\\\boxed{x=2}$