Question

Solve $\sqrt{3x^2+1}+\frac{4}{\sqrt{3x^2+1}}=5$

Answer 1

$\sqrt{3x^2+1}+\frac{4}{\sqrt{3x^2+1}}=5$
$3x^2+1+4=5\sqrt{3x^2+1}$
$(3x^2+1+4{)}^{{}^2}=(5{\sqrt{3x^2+1)}}^2$
$9x^4+25+30x^2=75x^2+25$
$9x^4=45x^2$
$x^4-5x^2=0$
$x^2\left(x^2-5\right)=0$
$x=0$ , $x=\pm \sqrt{5}$