Question

Ayuda xfavor
Cómo puedo resolver

Answer 1

$\sqrt{2x+3}+\sqrt{x-2}=4 \\ (\sqrt{2x+3}+\sqrt{x-2})^{2} =4^2\\\sqrt{2x+3}^2+2\sqrt{2x+3}*\sqrt{x-2}+\sqrt{x-2}^2=16\\2x+3+2\sqrt{(2x+3)(x-2)}+x-2=16\\3x+1+2\sqrt{(2x+3)(x-2)}=16\\3x+2\sqrt{(2x+3)(x-2)}=15\\(2\sqrt{(2x+3)(x-2)})^2=(15-3x)^2\\4(2x+3)(x-2)=225-90x+9x^2\\8x^2-4x-24=225-90x+9x^2\\0=249-86x+x^2\\(x-3)(x-83)=0\\x_1-3=0\\x_1=3\\x_2-83=0\\x_2=83\\\\\boxed{x_1=3 \ ,  x_2=83}$