Question #a5653

1 Answer
Feb 2, 2018

x=4+-2sqrt(2)

Explanation:

  1. Square both sides. (x+y)^2 = x^2 +2xy+y^2

(sqrt(3x-1) - sqrt(x-1))^2 = 2^2

3x-1-2sqrt((3x-1)*(x-1))+x-1=4

  1. Combine like terms and multiply.
    4x-2-2sqrt(3x^2-4x+1)=4

3.Divide by 2
2x-1-sqrt(3x^2-4x+1)=2

4.Subtract [2x-1] from both sides
-sqrt(3x^2-4x+1)=2-2x+1

5. Combine like terms and multiply by (-1)
sqrt(3x^2-4x+1)=2x-3

6.Square both sides.
3x^2-4x+1=4x^2-12x+9

7.subtract [4x^2-12x+9] and combine like terms.
-x^2+8x-8=0

8. Use the quadratic formula.
x=(-8+sqrt(64-32))/-2,x=(-8-sqrt(64-32))/-2

9.Simplify
x=4+2sqrt(2)," "4-2sqrt(2).