Question

Resolver a equação irracional : $\sqrt{1+x} + \sqrt{1-x} = 2$

Answer 1

Oi Yanca :)

$\sqrt{1+x}+ \sqrt{1-x}=2 \\ \\ \sqrt{1+x}=2-\sqrt{1-x} \\ \\ (\sqrt{1+x})^2=(2-\sqrt{1-x})^2 \\ \\ 1+x=4-4 \sqrt{1-x}+1-x \\ \\ 1+x-4-1+x=-4 \sqrt{1-x} \\ \\ 2x-4=-4 \sqrt{1-x} \\ \\ (2x-4)^2=(-4 \sqrt{1-x})^2$

$(2x-4)^2=(-4 \sqrt{1-x})^2 \\ \\ 4x^2-16x+16=16(1-x) \\ \\ 4x^2-16x+16=16-16x \\ \\ 4x^2-16x+16x+16-16=0 \\ \\ 4x^2=0 \\ \\ x^2= \frac{0}{4} \\ \\ x^2=0 \\ \\ \sqrt{x^2} = \sqrt{0} \\ \\ \boxed{x=0}$

Espero que goste. Comenta depois :)