Answer
The answer is : $x=(9+3\sqrt10+6\sqrt2+4\sqrt5)$.
Work Step by Step
Given:
$(2+\sqrt2)/(2-\sqrt2)=x/(3+\sqrt10)$
$\sqrt2(\sqrt2+1)/\sqrt2(\sqrt2-1)=x/(3+\sqrt10)$
$(\sqrt2+1)/(\sqrt2-1)=x/(3+\sqrt10)$
By cross multiplication we get,
$(\sqrt2+1)*(3+\sqrt10)=x*/(\sqrt2-1)$
$x*(\sqrt2-1)=(\sqrt2+1)*(3+\sqrt10)$
$x=((\sqrt2+1)*(3+\sqrt10))/(\sqrt2-1)$
Multiply and divide by ($\sqrt2+1$),
$x=((\sqrt2+1)*(3+\sqrt10))/(\sqrt2-1)*(\sqrt2+1)/(\sqrt2+1)$
$x=(\sqrt2+1)*(3+\sqrt10)*(\sqrt2+1)/(\sqrt2-1)*(\sqrt2+1)$
$x=(\sqrt2+1)^{2}*(3+\sqrt10)/(\sqrt2^{2}-1^{2})$
$x=(2+1+2\sqrt2)*(3+\sqrt10)$
$x=(3+2\sqrt2)*(3+\sqrt10)$
$x=(3*3+3*\sqrt10+2\sqrt2*3+2\sqrt2*\sqrt10)$
$x=(9+3\sqrt10+6\sqrt2+2\sqrt20)$
$x=(9+3*\sqrt2*\sqrt5+6\sqrt2+2\sqrt4*\sqrt5)$
$x=(9+3\sqrt10+6\sqrt2+4\sqrt5)$
