If $x \in \mathbb{R}$,then one of the solutions of $\sqrt{x+1}-|\sqrt{x-1}|=\sqrt{4x-1}$ among the following is

If the roots of the equation $x^2 + 2mx + m^2 - 2m + 6 = 0$ are equal,then the value of $m$ is:

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4-8x^3+11x^2+32x-60=0$ and $\alpha < \beta < \gamma < \delta$, then $4\alpha+3\beta+2\gamma+\delta=$

If $a, b$ are real numbers and $\alpha$ is a real root of $x^2 + 6x + 12 + 3 \sin(a + b\alpha) = 0$,then the value of $\cos(a + b\alpha)$ for the least positive value of $a + b\alpha$ is

The sum of all the real values of $x$ satisfying the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$ is