SOLUTION: Can someone please explain this? This was a challenge question from the instructor. √x - √(x - 5) = 1

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can someone please explain this? This was a challenge question from the instructor. √x - √(x - 5) = 1       Log On


   

Question 467547: Can someone please explain this? This was a challenge question from the instructor.
√x - √(x - 5) = 1

Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%29-sqrt%28x-5%29=1
square both sides
x-2sqrt%28x%29%2Asqrt%28x-5%29+%2Bx-5=1%5E2
2x-2sqrt%28x%29%2Asqrt%28x-5%29=1%2B5
+%282x-6%29=+2+sqrt%28x%29%2Asqrt%28x-5%29
square both side
%282x-6%29%5E2=+4x%28x-5%29
4x%5E2-24x%2B36=4x%5E2-20x
-24x+20x=-36
-4x=-36
x=9


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Can someone please explain this? This was a challenge question from the instructor.
√x - √(x - 5) = 1
----
Square both sides to get:
x - 2sqrt(x^2-5x) + (x-5) = 1
----
2x-2sqrt(x^2-5x) = 6
---
-2sqrt(x^2-5x) = -2x+6
----
-sqrt(x^2-5x) = -x+3
---
Square both sides to get:
x^2-5x = x^2-6x+9
----
x = 9
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Cheers,
Stan H.
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