I am trying to solve below question from Coursera Intro to Calculus (link)
A right-angled triangle has shorter side lengths exactly $a^2-b^2$ and $2ab$ units respectively, where $a$ and $b$ are positive real numbers such that $a$ is greater than $b$. Find an exact expression for the length of the hypotenuse (in appropriate units).
Below are the choices
$(a - b)^2$
$\sqrt(a^4 + 4a^2b^2 -b^4)$
$a^2 + b^2$
$\sqrt(a^2 + 2ab -b^2)$
$(a + b)^2$
When I attempt to work out the solution (and I even got a 2nd pair of eyes to look at it, but he arrived at the same conclusion), I get this:
$(a^2 - b^2)^2 + (2ab)^2 = x^2$
$a^4 -2a^2b^2 + b^4 + (2ab)^2 = x^2$
$a^4 -2a^2b^2 + b^4 + 4a^2b^2 = x^2$
$a^4 + 2a^2b^2 + b^4 = x^2$
$\sqrt(a^4 + 2a^2b^2 + b^4) = x$
Please help! How to get the correct solution?