Question #a5653

1 Answer
landon3 · EZ as pi
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).#

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