Question

$x+\sqrt{x}=\frac{6}{25}$ find the value of $x^2.$

Answer 1

$x+\sqrt{x}=\frac{6}{25}$

$x\cdot 25+\sqrt{x}\cdot 25=6$

$25\sqrt{x}=6-25x$

squaring on both sides

$625x=36-300x+625x^2$

$625x^2-925x+36=0$

solving the above quadratic equation, we get

$x=\frac{1}{25}$

$\therefore x^2=\frac{1}{625}$