Solve for c: ​

We split the equations:

(1) $\sqrt{4+\sqrt{8+4c}}=2$

(2) $\sqrt{2+\sqrt{2+c}}=2\sqrt{2}$

 

Square both sides of both equations:

(1) $4+\sqrt{8+4c}=4$

(2) $2+\sqrt{2+c}=8$

 

Simplify and square both sides of both equations once again:

(1) $8+4c=0$

(2) $2+c=36$

 

We get:

$c=-2$ and $c=34$

 

That is incorrect, because $c$ needs to be the same value for the equations to work.

By commutative property, we get another two equations:

(3) $\sqrt{4+\sqrt{8+4c}}=2\sqrt{2}$

(4) $\sqrt{2+\sqrt{2+c}}=2$

 

Square both sides of both equations:

(3) $4+\sqrt{8+4c}=8$

(4) $2+\sqrt{2+c}=4$

 

Simplify and sqaure both sides of both equations once again:

(3) $8+4c=16$

(4) $2+c=4$

 

For both equations, we get $\boxed{c=2}$

 

Take that! Guest!