Question 101464
(X+1)^1/2+(2X)^1/2=1
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(X+1)^1/2 = -(2X)^1/2+1
Square both sides:
x+1 = 2x+1 -2(2x)^(1/2)
x=2(2x)^(1/2)
Square both sides:
x^2 = 4(2x)
x^2-8x=0
x(x-8)=0
x=0 or x=8
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Check the answrs in (X+1)^1/2+(2X)^1/2=1
If x=0: sqrt(1)+ sqrt(0) = 1
True 
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If x=8: sqrt(9)+sqrt(16)=1
False
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Only solution: x=0
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Cheers,
Stan H.