document.write( "Question 914044: If b+c-a/a, c+a-b/b, a+b-c/c are in A.P.\r
\n" ); document.write( "\n" ); document.write( "Prove that 1/a,1/b,1/c are also in A.P
\n" ); document.write( "

Algebra.Com's Answer #554851 by mananth(16946)\"\" \"About 
You can put this solution on YOUR website!
b+c-a/a, c+a-b/b, a+b-c/c in AP\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+%28c%2Ba-b%29%2Fb+-+%28b%2Bc-a%29%2Fa+=+%28a%2Bb-c%29%2Fc+-+%28c%2Ba-b%29%2Fb\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+%28a%28c%2Ba-b%29+-+b%28b%2Bc-a%29%29%2Fab+=+%28b%28a%2Bb-c%29-c%28c%2Ba-b%29%29%2Fbc\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28ac%2Ba%5E2-ab-b%5E2-bc%2Bab%29%2Fab+=+%28ab%2Bb%5E2-bc-c%5E2-ac%2Bbc%29%2Fbc\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28a%5E2-b%5E2%2Bac-bc%29%2Fab+=+%28+b%5E2-c%5E2%2Bab-ac%29%2Fbc\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28%28a%2Bb%29%28a-b%29%2Bc%28a-b%29%29%2Fab=%28%28b%2Bc%29%28b-c%29%2Ba%28b-c%29%29%2Fbc\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28%28a-b%29%28a%2Bb%2Bc%29%29%2Fab=+%28%28b-c%29%28a%2Bb%2Bc%29%29%2Fbc\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28a-b%29%2Fa=+%28b-c%29%2Fc\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "ac-bc = ab-ac\r
\n" ); document.write( "\n" ); document.write( "/abc\r
\n" ); document.write( "\n" ); document.write( "1/b -1/a = 1/c-1/b\r
\n" ); document.write( "\n" ); document.write( "Hence they are in AP\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );