Question

Question #a5653

Answer 1

`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).`