If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b^{2}=0$,then $\alpha^{2}+\beta^{2}$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 - x - 1 = 0$,then find the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2-4x+5=0$,then the quadratic equation whose roots are $\alpha^2+\beta$ and $\alpha+\beta^2$ is

If $a, b$ and $c$ are the roots of $x^3+qx+r=0$,then $(a-b)^2+(b-c)^2+(c-a)^2=$ (in $q$)

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Rahul made a mistake in writing down the coefficient of $x$ and ended up with roots $(3, 2)$. The correct roots of the equation are:

If the equation having the roots as the values obtained by diminishing each root of the equation $x^3-3x^2+2x-1=0$ by $K$ is $x^3-x-1=0$,then $K=$