SOLUTION: log(x + y) = log 3 + 1/2 log x + 1/2 log y prove x^2 + y^2 = 7xy

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Question 768913: log(x + y) = log 3 + 1/2 log x + 1/2 log y
prove x^2 + y^2 = 7xy

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%28x+%2B+y%29+=+log+%283%29+%2B+%281%2F2%29+log%28+x%29+%2B+%281%2F2%29+log+%28y%29...writ right side equation as a single logarithm

log%28x+%2B+y%29+=+log+%283%29+%2B++log%28+x%5E%281%2F2%29%29+%2B+log+%28y%5E%281%2F2%29%29
log%28x+%2B+y%29+=+log+%283%29+%2B++log%28+sqrt%28x%29%29+%2B+log+%28sqrt%28y%29%29

log%28x+%2B+y%29+=+log+%283%2Asqrt%28x%29%29+%2B+log+%28sqrt%28y%29%29

log%28x+%2B+y%29+=+log+%283%2Asqrt%28x%29%2Asqrt%28y%29%29

log%28x+%2B+y%29+=+log+%283%2Asqrt%28xy%29%29....if log same, then

x+%2B+y+=+3%2Asqrt%28xy%29.....square both sides

%28x+%2B+y%29%5E2+=+9%2A%28sqrt%28xy%29%29%5E2

x%5E2%2B2xy+%2B+y%5E2+=+9xy

x%5E2%2B+y%5E2+=+9xy-2xy+

x%5E2%2B+y%5E2+=7xy+