If $\log _{10}(x^{2}-6x+45)=2$,then the values of $x$ are

The number of integral values of $a$ for which $x^2 - (a - 1)x + 3 = 0$ has both roots positive and $x^2 + 3x + 6 - a = 0$ has both roots negative is

If the roots of the equation $lx^2 + nx + n = 0$ are in the ratio $p:q$,then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{n}{l}} = $

Solve the given two equations and select the correct option.
$I.$ $x^{2}-5x+6=0$
$II.$ $2y^{2}-15y+27=0$

Solve the given two equations and select the correct option.
$I. x = \sqrt[3]{357911}$
$II. y = \sqrt{5041}$

The solution set of the equation $x^{\log_x(1 - x)^2} = 9$ is