Question

Raiz de x+1 + raiz 3x =5 qual a resposta desta equação irracional

Answer 1

$\sqrt{x + 1} + \sqrt{3x } = 5 \\ {( \sqrt{x + 1} + \sqrt{3x} ) }^{2} = {5}^{2} \\ x + 1 + 2 \sqrt{(x + 1)} \sqrt{3x} + 3x = 25 \\ x + 1 + 3x + 2 \sqrt{(x + 1)} \sqrt{3x} = 0 \\ 4x + 1 + 2 \sqrt{3x(x + 1)} = 25 \\ 2 \sqrt{3x(x + 1)} = 25 - 4x - 1 \\ 2 \sqrt{3x(x + 1)} = - 4x + 24 \\ \sqrt{3x(x + 1)} = - 2x + 12 \\ {(\sqrt{3x(x + 1)})}^{2} = {( - 2x + 12)}^{2} \\ 3x(x + 1) = {4x}^{2} - 48x + 144 \\ {3x}^{2} + 3x = {4x}^{2} - 48x + 144 \\ {x}^{2} - 51x + 144 \\ (x - 48)(x - 3) = 0 \\ x = 48 \\ x = 3$