If $x+\frac{1}{x}=a$ and $x^2+\frac{1}{x^3}=b$,then $x^3+\frac{1}{x^2}$ is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4+x^2+1=0$,then $\frac{\alpha^3+\beta^3+\gamma^3+\delta^3}{\alpha^6+\beta^6+\gamma^6+\delta^6}=$

The number of ordered pairs $(x, y)$ of real numbers that satisfy the simultaneous equations $x+y^2=x^2+y=12$ is

$\sqrt{x + 2\sqrt{x - 1}} + \sqrt{x - 2\sqrt{x - 1}} = $

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,and $\alpha + \beta$,$\alpha^2 + \beta^2$,and $\alpha^3 + \beta^3$ are in a geometric progression,and $\Delta = b^2 - 4ac$,then which of the following is true?

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta$ $(\beta > \alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots,then a possible value of $\gamma$ is