Question

Sa se determine solutiile reale ale ecuatiei √2+x=x.

Answer 1

$\sqrt{x+2}=x \Rightarrow x \geq 0. \\ \\ Ridicam~la~patrat~si~obtinem: \\ \\ x+2=x^2 \\ \\ x^2-x-2=0 \\ \\ \Delta=b^2-4ac=(-1)^2-4 \cdot1 \cdot (-2)=1+8=9. \\ \\ x_{1,2}= \frac{-b \pm \sqrt{ \Delta}}{2a}= \frac{1 \pm 3}{2} . \\ \\ Dar~x \geq 0 \Rightarrow \boxed{x=2}~.$

Answer 2

√(x+2)=x
x+2=x^2
x^2-x=2
x=2