Question

Calcule x :

√x + 5 - √x-3 = x-2

Answer 1

$( \sqrt{x+5})^2-( \sqrt{x+3})^2=(x-2)^2 \\ \\ x+5-x+3=x^2-4x+4 \\ \\ x^2-4x-4=0 \\ \\ x= \frac{4+- \sqrt{16+16} }{2.1} = \frac{4+- \sqrt{32} }{2} = \frac{4+-4 \sqrt{2} }{2}= \\ \\ x_{1}= \frac{4+4 \sqrt{2} }{2}=2+2 \sqrt{2} \\ \\ x_{2}= \frac{4-4 \sqrt{2} }{2}=2-2 \sqrt{2}$

Answer 2

Basta organizarmos e calcularmos.

√x + 5 - √x - 3 = x - 2
√x - √x + 5 - 3 = x - 2
2 = x - 2
x - 2 = 2
x = 2 + 2

x = 4