document.write( "Question 1121372: if y is the mean proportional between x and z ; show that xy + yz is the mean proportional between x² + y² and y² + z² \n" ); document.write( "

Algebra.Com's Answer #737265 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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if y is the mean proportional between x and z ;
\n" ); document.write( "We know:
\n" ); document.write( " $\"x%2Fy\"$ = $\"y%2Fz\"$ ; $\"y+=+sqrt%28xz%29\"$
\n" ); document.write( ":
\n" ); document.write( " show that xy + yz is the mean proportional between x² + y² and y² + z²
\n" ); document.write( " $\"%28x%5E2%2By%5E2%29%2F%28xy%2Bzy%29\"$ = $\"%28xy%2Bzy%29%2F%28y%5E2%2Bz%5E2%29\"$
\n" ); document.write( "The easiest to show this is to give some values to x & z
\n" ); document.write( "x=2; z=18; then y = $\"sqrt%282%2A18%29\"$ = 6
\n" ); document.write( ":
\n" ); document.write( " $\"%284%2B36%29%2F%2812%2B108%29\"$ = $\"%2812%2B108%29%2F%2836%2B324%29\"$
\n" ); document.write( " $\"40%2F120\"$ = $\"120%2F360\"$ \n" ); document.write( "

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