Question

If the value of real number $a>0$ for which $x^2-5ax+1-0$ and $x^2-ax-5-0$ have a common real root is $\frac{3}{\sqrt{2\beta }}$ then $\beta$ is equal to_______

Answer 1

Answer: 13

Two equations have common root
$\therefore (4a)(26a)=(-6{)}^2=36$
$\Rightarrow a^2=\frac{9}{26}$
$\therefore a=\frac{3}{\sqrt{26}}$
$\Rightarrow \beta =13$