The solution of the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{3x}{p + q + r} = 0$ is

If the roots of the equation $({p^2} + {q^2}){x^2} - 2q(p + r)x + ({q^2} + {r^2}) = 0$ are real and equal,then $p, q, r$ will be in:

The number of solutions of the equation $\sqrt{3x^2+x+5} = x-3$ is

The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is

If the roots of $x^4+x^3-4x^2+x+1=0$ are diminished by $\alpha$ or $\beta$,then the equation with the diminished roots does not contain the $x^2$ term. Then $12(\alpha-\beta)^2=$

The roots of the equation $x^4+x^3-4x^2+x+1=0$ are diminished by $h$ so that the transformed equation does not contain the $x^2$ term. If the values of such $h$ are $\alpha$ and $\beta$,then $12(\alpha-\beta)^2=$