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A Real Number problem (Posted on 2006-08-16) Difficulty: 2 of 5
Given that x is a real number, determine all possible solutions of:
√(x-1) + √(3-x) = x² - 4x + 6

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

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Some Thoughts An idea | Comment 1 of 9
Given that sqrt(x-1)+sqrt(3-x)= sqrt(2+ 2.sqrt((x-1)(3-x))), writing f for x^2-4x+6, you would have to solve 2+2.sqrt((x-1)(3-x))=f^2, or (x-1)(3-x)= (f^2-2)^2, an eight-degree polynomial... 
  Posted by Old Original Oskar! on 2006-08-16 13:36:40
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