SOLUTION: {{{sqrt(3x) - sqrt(3x-5) = 1}}} x = ?

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Question 204498: sqrt%283x%29+-+sqrt%283x-5%29+=+1
x = ?
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
square both sides of the equation
sqrt%283x%29+-+sqrt%283x-5%29+=+1
%28sqrt%283x%29+-+sqrt%283x-5%29%29%5E2+=+%281%29%5E2
3x+-+2%2Asqrt%283x%2A%283x-5%29%29+%2B+3x+-+5+=+1
3x+%2B+3x+-+5+-+1+=+2%2Asqrt%283x%2A%283x-5%29%29
6x+-+6+=+2%2Asqrt%283x%2A%283x-5%29%29
square them again:
%286x+-+6%29%5E2+=+%282%2Asqrt%283x%2A%283x-5%29%29%29%5E2
36x%5E2+-+72x+%2B+36+=+4%2A3x%2A%283x-5%29
36x%5E2+-+72x+%2B+36+=+36x%5E2+-+60x
36x%5E2+-+72x+%2B+36+-+36x%5E2+%2B+60x+=+0
-12x+%2B+36+=+0
12x = 36
x = 36/12 = 3