document.write( "Question 26172: if x and y are positive real numbers, use the fact that t+(1/t)>=2 for positive numbers to show that (x+y)(xy+1)>=4xy. \n" ); document.write( "

Algebra.Com's Answer #14349 by venugopalramana(3286) $\"\"$ $\"About$

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if x and y are positive real numbers, use the fact that t+(1/t)>=2 for positive numbers to show that
\n" ); document.write( "TST. (x+y)(xy+1)>=4xy.
\n" ); document.write( "SINCE X AND Y ARE POSITIVE DIVIDE BOTH SIDES BY XY
\n" ); document.write( "TST. (x+y)(xy+1)/XY>=4
\n" ); document.write( "TST. {(x+y)/X}{(xy+1)/Y}>=4
\n" ); document.write( "LHS=(1+Y/X)(X+1/Y)
\n" ); document.write( "=X+1/Y+Y+1/X=(X+1/X)+(Y+1/Y)>=2+2=4
\n" ); document.write( "AS PER THE GIVEN RELATION
\n" ); document.write( "t+(1/t)>=2 \n" ); document.write( "

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