SOLUTION: Sqrt2x-1=sqrtx-1 +1

Question 670704: Sqrt2x-1=sqrtx-1 +1
Found 2 solutions by edjones, swincher4391:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
sqrt(2x-1)=sqrt(x-1)+1
2x-1=(a+1)^2 Square each side; let a=sqrt(x-1)
...=a^2+2a+1
...=x-1+2sqrt(x-1)+1
2x-1=x+2sqrt(x-1)
x-1=2sqrt(x-1)
x^2-2x+1=4(x-1)
...=4x-4
x^2-6x+5=0
(x-5)(x-1)=0
x=5, x=1
.
Ed
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!

Square both sides:

2x-1 = x-1 + 2sqrt(x-1) + 1
2x -1 = x + 2sqrt(x-1)

x -1 = 2sqrt(x-1)
Square both sides again:
x^2 - 2x + 1 = 4(x-1)
x^2 - 2x + 1 = 4x-4
x^2 -6x +5 = 0
(x-1)(x-5)
x = 1,5

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