Question

Hi, I'm totally stuck!
Problem: sqrt(x-3) = sqrt (2) -sqrt(x)

I know I square them to get them out of square roots but after that I'm stuck-
answers: -25/8
25/8
no solution
1/8
Please show me how its done
Thank you

Answer 1

x - 3 = 2 - x
add x to both sides
2x - 3 = 2
Add 3 to both sides
2x = 5
divide by 2
x = 2.5

Answer 2

square both sides

x-3 = 2 - 2√(2x) + x
2√(2x) = 5
√2x = 5/2
square again
2x = 25/4
x = 25/8

BUT, since we squared our equation, we have to verfify each answer

LS = √(3-25/8) = appr. .3536
RS = √2 - √(25/8) = appr. -.3536

so LS ≠ RS, and thus there is NO SOLUTION.

Answer 3

Thank you