Question

Show that ((7+3sqrt5)/(sqrt2+sqrt7+3sqrt5)+((7-3sqrt5)/(sqrt2+sqrt7-3sqrt5))=2sqrt2

Answer 1

Perhaps, condition is incorrect:

$\dfrac{(7+3\sqrt5)}{(\sqrt2+\sqrt7+3\sqrt5)}+\dfrac{(7-3\sqrt5)}{(\sqrt2+\sqrt7-3\sqrt5)}=2\sqrt2$

$\dfrac{(7+3\sqrt5)}{(\sqrt2+\sqrt7+3\sqrt5)}+\dfrac{(7-3\sqrt5)}{(\sqrt2+\sqrt7-3\sqrt5)}\approx$ $1.162845244$

$2\sqrt2\approx$ $2.828427124$