Question

Resolva a questão:√3x+1+√5x=√16+1

Answer 1

$\sqrt{3x+1}+\sqrt{5x}=5$

Dominio

$3x+1\geq0 \wedge 5x\geq0$

$x\geq-\frac{1}{3} \wedge x\geq0 \Longleftrightarrow x\geq0$

Resolvamos

$\sqrt{3x+1}=5-\sqrt{5x}$

$\sqrt{3x+1}^2=\left(5-\sqrt{5x}\right)^2$

$3x+1= 25+5x-10\sqrt{5x}$

$2x+24= 10\sqrt{5x}$

$x+12= 5\sqrt{5x}$

$(x+12)^2= (5\sqrt{5x})^2$

$x^2+24x+144= 125x$

$x^2-101x+144= 0$

Aplicamos la fórmula general

$x_{1,2}=\frac{101\pm5\sqrt{385}}{2}$