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The equation sqrt(x + 1) - sqrt(x - 1) = sqrt(4x - 1) has how many real solutions?
- No solution
- One solution
- Two solution
- More than two solutions
Correct answer: No solution
Solution
After squaring, we get 2x - 2*sqrt(x²-1) = 4x - 1, i.e., 1 - 2x = 2*sqrt(x²-1). Since x >= 1, left side 1 - 2x <= -1 < 0, while right side >= 0. No solution exists.
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