radical equations: sqrt(a - 10) = sqrt(a + 6) + 8

[chickyme89]

I need help solving this equation.

The problem:

sqrt(a-10)=sqrt(a+6)+8

This is the work that I have tried, but without a correct answer:

a - 10 = (a + 6) + (8sqrt(a + 6) + 8sqrt(a + 6) + 64

a - 10 + a + 6 + 16sqrt(a + 6) + 64

a = a + 80 + 16sqrt(a + 6)

-80 = 16sqrt(a + 6)

640 = 256(a + 6)

640/256 = a + 6

5/2-6/1=a

5/2 - 12/2 = a

a = -7/2

Any help would be appreciated.

 

[Denis]

Hey Chicky, -80 squared = 6400, not 640 :wink:

 

[chickyme89]

OH MAN! no wonder...i tried it again and got a whole different answer and i was freaking out. Thanks man. Hey, can anyone tell me if these steps are right?

6400=256(a+6)
6400=256a+1536
4864=256a
19=a

I'm just thinking that I should have come up with something other than a whole number.

I also have another problem that I am dying to figure out, but can't.

The problem:
(c+1)^(2/3)-2(c+1)^(1/3)-15=0

 

[Denis]

(c+1)^(2/3) - 2(c+1)^(1/3) - 15 = 0

let x = c+1: x^(2/3) - 2x^(1/3) - 15 = 0
factor directly:
(x^(1/3) - 5)(x^(1/3) + 3) = 0

x^(1/3) = 5 or x^(1/3) = -3
x = 125 or x = -27

resubstitute x = c+1; ok?

 

[chickyme89]

Thank you truly for all of your help.