Expert: Socrates - 9/27/2006

Question
The square root of x-3 plus the square root of x =5

I figure the answer is no solution, but I figured you could lead me in the right path.

The questions asks to find all solutions using algebra skills

Answer
(x-3)^1/2  + x^1/2  = 5

square both sides

(x-3) + x + (2)(x-3)^1/2 x^1/2  = 25

simplify

(2)(x-3)^1/2 x^1/2 = 28 - 2x

(x-3)^1/2 x^1/2 = 14 - x

square both sides again to finally get rid of all the square roots

(x-3)(x) = 196 - 28x + x^2

simplify

x^2 - 3x = 196 - 28x + x^2

- 3x = 196 - 28x

25x = 196

x = 196/25


Checking this answer in the original equation, you find that x = 196/25 is not a solution. Therefore, there are no solutions.