x^2+y^2=10xy show that 2log(x+y)=logx+logy+2log2+log3
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Answered by
109
Given x² + y² = 10x
=> x² + y² + 2xy = 10x + 2xy
=> ( x + y )² = 12xy
Take log bothside of the equation ,
log ( x + y )² = log ( 12xy )
=> 2log( x + y ) = log 12 + log x + log y
=> 2log(x+y) = log(2²×3)+logx+logy
=> 2log(x+y)=log2²+log3+logx+logy
=>2log(x+y)=2log2+log3+logx+logy
•••••
=> x² + y² + 2xy = 10x + 2xy
=> ( x + y )² = 12xy
Take log bothside of the equation ,
log ( x + y )² = log ( 12xy )
=> 2log( x + y ) = log 12 + log x + log y
=> 2log(x+y) = log(2²×3)+logx+logy
=> 2log(x+y)=log2²+log3+logx+logy
=>2log(x+y)=2log2+log3+logx+logy
•••••
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53
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