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Question

Square root x - square root x-5 =1

Answer 1

√x - √(x - 5) = 1

√x = 1 + √(x - 5)                add √(x - 5) to both sides

x = 1 + 2√(x - 5) + x - 5     square both sides

0 = -4 + 2√(x - 5)               subtract x from both sides, combine

4 = 2√(x - 5)                       add four to both sides

2 = √(x - 5)                         divide both sides by 2

4 = x - 5                              square both sides

9 = x                                   add five to both sides

 

Check:

√9 - √(9 - 5) = 1

3 - 2 = 1

Answer 2

sqrt(x) - sqrt(x-5) = 1   Square both sides

 

x -2(sqrt(x²-5x) + x - 5 = 1  Isololate the sqrt

 

sqrt(x²-5x) = -x + 3   Square both sides again

 

x² - 5x = x²-6x + 9

 

x = 9