If $x + \sqrt {({x^2} + 1)} = a,$ then $x =$
${1 \over 2}(a + 1/a)$
${1 \over 2}(a - 1/a)$
$(a + {a^{ - 1}})$
None of these
If $x = \sqrt 7 + \sqrt 3 $ and $xy = 4,$then ${x^4} + {y^4}=$
The value of the fifth root of $10^{10^{10}}$ is
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $
If ${\left( {{2 \over 3}} \right)^{x + 2}} = {\left( {{3 \over 2}} \right)^{2 - 2x}},$then $x =$
${{12} \over {3 + \sqrt 5 - 2\sqrt 2 }} = $