Esercizio
$\sqrt{x+2}-\sqrt{2x+2}+1=0$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. (x+2)^(1/2)-(2x+2)^(1/2)+1=0. Applicare la formula: x+a=b\to x=b-a, dove a=-\sqrt{2x+2}+1, b=0, x+a=b=\sqrt{x+2}-\sqrt{2x+2}+1=0, x=\sqrt{x+2} e x+a=\sqrt{x+2}-\sqrt{2x+2}+1. Applicare la formula: -\left(a+b\right)=-a-b, dove a=-\sqrt{2x+2}, b=1, -1.0=-1 e a+b=-\sqrt{2x+2}+1. Applicare la formula: x^a=b\to \left(x^a\right)^{inverse\left(a\right)}=b^{inverse\left(a\right)}, dove a=\frac{1}{2}, b=\sqrt{2x+2}-1, x^a=b=\sqrt{x+2}=\sqrt{2x+2}-1, x=x+2 e x^a=\sqrt{x+2}. Applicare la formula: \left(a+b\right)^2=a^2+2ab+b^2, dove a=\sqrt{2x+2}, b=-1 e a+b=\sqrt{2x+2}-1.
(x+2)^(1/2)-(2x+2)^(1/2)+1=0
Risposta finale al problema
$x=7$