+0

# Solve for c: ​

+1
55
2
+337

Solve for c: $$\sqrt{4+\sqrt{8+4c}}+ \sqrt{2+\sqrt{2+c}} = 2+2\sqrt{2}$$

Apr 4, 2020

#1
-1

c = 4.

Apr 4, 2020
#2
+633
+2

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!

Apr 5, 2020