If $x = \sqrt{7} + \sqrt{3}$ and $xy = 4$,then $x^4 + y^4 =$

Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?
$I$. It has at least one negative root.
$II$. It has at least one positive root.
$III$. Both its roots are real.

The roots of the equation $x^2 - 2\sqrt{2}x + 1 = 0$ are:

Suppose the height of a pyramid with a square base is decreased by $p \%$ and the lengths of the sides of its square base are increased by $p \%$ (where $p > 0$). If the volume remains the same,then:

In $\triangle ABC$,the value of $\angle A$ is obtained from the equation $3 \cos A + 2 = 0$. The quadratic equation,whose roots are $\sin A$ and $\tan A$,is

Both the roots of the given equation $(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0$ are always