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Question 69100: sqrt(x + 4) + sqrt(x - 1) = 5
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! sqrt(x + 4) + sqrt(x - 1) = 5
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Subtract Sqrt(x-1) from both sides:
Sqrt(x+4) = 5 - Sqrt(x-1)
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Square both sides; FOIL (5-Sqrt(x-1)(5-Sqrt(x-1); results:
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x + 4 = 25 - 5*Sqrt(x-1) - 5*Sqrt(x-1) + (x-1)
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x + 4 = 25 - 10*Sqrt(x-1) + x - 1; remove the brackets
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x + 4 = 25 - 1 + x - 10Sqrt(x-1)
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x + 4 = 24 + x - 10Sqrt(x-1)
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x - x + 4 - 24 = -10Sqrt(x-1); get Sqrt on the right by itself
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-20 = -10Sqrt(x-1)
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Square both sides again, gets rid of the last radical and you have:
+400 = +100(x-1)
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400 = 100x - 100
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400 + 100 = 100x
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500 = 100x
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5 = x
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Check solution x = 5 in original equation:
sqrt(x + 4) + sqrt(x - 1) = 5
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sqrt(5 + 4) + sqrt(5 - 1) = 5
:
sqrt(9) + sqrt(4) = 5
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