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 #737275 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "We are given that

\n" ); document.write( " $\"x%2Fy+=+y%2Fz\"$

\n" ); document.write( "or

\n" ); document.write( "(1) $\"y%5E2+=+xz\"$

\n" ); document.write( "Then we are to show that

\n" ); document.write( "(2) $\"%28x%5E2%2By%5E2%29%2F%28xy%2Byz%29+=+%28xy%2Byz%29%2F%28y%5E2%2Bz%5E2%29\"$

\n" ); document.write( "The algebra for the general case is not terribly difficult....

\n" ); document.write( "Equation (2) is equivalent to

\n" ); document.write( " $\"%28xy%2Byz%29%5E2+=+%28x%5E2%2By%5E2%29%28y%5E2%2Bz%5E2%29\"$

\n" ); document.write( "Then using equation (1) where appropriate....

\n" ); document.write( " $\"%28y%28x%2Bz%29%29%5E2+=+%28x%5E2%2By%5E2%29%28y%5E2%2Bz%5E2%29\"$

\n" ); document.write( " $\"%28y%5E2%29%28x%2Bz%29%5E2+=+%28x%5E2%2By%5E2%29%28y%5E2%2Bz%5E2%29\"$

\n" ); document.write( " $\"%28xz%29%28x%2Bz%29%5E2+=+%28x%5E2%2Bxz%29%28xz%2Bz%5E2%29\"$

\n" ); document.write( " $\"%28xz%29%28x%2Bz%29%5E2+=+%28x%29%28x%2Bz%29%28z%29%28x%2Bz%29\"$

\n" ); document.write( " $\"%28xz%29%28x%2Bz%29%5E2+=+%28xz%29%28x%2Bz%29%5E2\"$

\n" ); document.write( "Done...! \n" ); document.write( "

\n" );