If $x-\frac{1}{x}=\sqrt{21},$ then the value of $\left(x^{2}+\frac{1}{x^{2}}\right)\left(x+\frac{1}{x}\right)$ will be

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{25} x + \sqrt{16} y = 41$
$II.$ $\sqrt{16} x + \sqrt{25} y = 40$

The condition for the roots of the equation $(c^2 - ab)x^2 - 2(a^2 - bc)x + (b^2 - ac) = 0$ to be equal is

The expression $x^2-x+1$ has:

The value of $x$ in the given equation $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$ is

If $\alpha$ and $\beta$ are the roots of the equation $6x^2 - 5x + 1 = 0$,then the value of $\tan^{-1} \alpha + \tan^{-1} \beta$ is: