√2х-1 = √х-3

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To solve this equation, we first need to isolate one of the square roots.
√2x - 1 = √x - 3
Add 1 to both sides:
√2x = √x - 2
Next, square both sides to eliminate the square root:
(√2x)^2 = (√x - 2)^2
2x = x - 4√x + 4
Now, isolate x by moving all terms to one side:
2x - x = -4√x + 4
x = -4√x + 4
Lastly, we can square both sides one more time to eliminate the square root:
x^2 = 16x - 32
Rearrange into a quadratic equation:
x^2 - 16x + 32 = 0
This equation can be factored or solved using the quadratic formula.