1. ## Radical Pythagorean Theorem

I'm stumped on this.
New problem!

Original:
x^2 + (x+5)^2 =(5√5)^2

Now, I tried canceling out the radical. That gives me "0" for C when factoring, though, so it doesn't work out ( I believe).

Doing 5^2 * 5 gives me 625, which gives me x=-20, 15 after factoring. Doesn't check out.

2. If you notice:

$(5\sqrt{5})^2 = 5^2(\sqrt{5})^2 = 25*5 = 125$

So, now you have:

$x^2 + (x + 5)^2 = 125$

$2x^2 + 10x + 25 = 125$

$2x^2 + 10x = 100$

$2x^2 + 10x - 100 = 0$

$x^2 + 5x - 50 = 0$

Just solve that and you should have your answer.

3. Originally Posted by tyler.
i'm stumped on this.
New problem!

Original:
X^2 + (x+5)^2 =(5√5)^2

now, i tried canceling out the radical. That gives me "0" for c when factoring, though, so it doesn't work out ( i believe).

Doing 5^2 * 5 gives me 625, which gives me x=-20, 15 after factoring. Doesn't check out.
5^2 * 5 = 5^3 = 125

x^2 + x^2 + 10x + 25 = 125

2x^2 + 10x - 100 = 0

x^2 + 5x - 50 = 0

and solve

4. D'oh! I tried thinking that you should distrubute the square - but to the radicand even after simplifying. That was my big problem!

Thanks a ton! This has been making me want to cry =P