Question

raiz quadrada de 5x + raiz quadrada de x + 2 = 3

Answer 1

√(5x) +√(x + 2) = 3

5x = [3 -√(x + 2)]²

$(a -b)^{2} = a^{2} -2ab + b^{2}$

5x = 9 -6√(x + 2) +x + 2

5x -x -11 = -6√(x + 2)

[(4x -11)/-6]² = √(x + 2)²

(16x² -88x +121)/36 = x + 2

16x² -88x +121 = 36x + 72

16x² -124x +49 = 0

$\Delta = \mathsf {b^2-4ac }$

15376 -4 * 784 = 12240 = 12² * 85

$\mathsf{x = \frac{-b \pm \sqrt{\Delta} }{2a}}$

124 ± 12√85/32

31 ± 3√85/8

{31 + 3√85/8 , 31 - 3√85/8}