Question 55943: Could you please help me solve, sqrt(2+4x) + sqrt(3-4x)=3
Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! sqrt(2+4x) + sqrt(3-4x)=3
Square both sides to get:
2+4x + 2sqrt[(2+4x)(3-4x)] + 3-4x = 9
5 + 2sqrt[6+4x-16x^2] = 9
sqrt[6+4x-16x^2] =2
Square both sides again:
6+4x-16x^2= 4
16x^2-4x-2=0
(2x-1)(8x+2)=0
x=1/2 or x=1/4
Checking these answers in the original problem:
If x=1/2, sqrt(2+2) + sqrt(3-2)=3
True
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If x=1/4, sqrt(2+1) + sqrt(3-1)=3
False
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The only solution is x=1/2
Cheers,
Stan H.
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