https://postimg.org/image/epnzx6clr/
I couldn't solve that and need help.
https://postimg.org/image/epnzx6clr/
I couldn't solve that and need help.
yes, the sum of x's is $(6+2\sqrt{2})+(6-2\sqrt{2}) = 12$
First, I drew a picture to draw in an auxiliary line segment & label some variables ...
equations I came up with using Pythagoras & similar triangles ...
$x^2+2^2=(b\sqrt{2})^2$
$a^2+b^2=12^2$
$x^2+14^2 = (a+b)^2$
$\dfrac{x}{a+b}=\dfrac{b}{12}$
Found an equation quadratic in $x$ and solved ...
using the first Pythagoras equation, $b^2 = \dfrac{x^2+4}{2}$
using the second & third Pythagoras equations, $x^2+14^2 = 12^2 + 2ab \implies ab = \dfrac{x^2+52}{2}$
using the proportion from similar triangles, $12x = ab+b^2$
substitute for $ab$ and $b^2$ ... you get an equation quadratic in $x$
I will disturb you one more time.
https://postimg.org/image/rzkw43x1l/