document.write( "Question 252008: if x=c*y+b*z
\n" ); document.write( " y=a*z+c*x
\n" ); document.write( " z=b*x+a*y
\n" ); document.write( "Then prove that x^2/1-a^2=y^2/1-b^2=z^2/1-c^2
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Algebra.Com's Answer #184415 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "if \"x=cy%2Bbz\"
\n" ); document.write( " \"y=az%2Bcx\"
\n" ); document.write( " \"z=bx%2Bay\"
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\n" ); document.write( "Then prove that \"x%5E2%2F%281-a%5E2%29=y%5E2%2F%281-b%5E2%29=z%5E2%2F%281-c%5E2%29\"
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document.write( "Solve the second for c:\r\n" );
document.write( "\"y=az%2Bcx\"\r\n" );
document.write( "\"y-az=cx\"\r\n" );
document.write( "\"%28y-az%29%2Fx=c\"\r\n" );
document.write( "Use the third equation to substitute for z\r\n" );
document.write( "\"%28y-a%28bx%2Bay%29%29%2Fx%7D=c%7D%7D%0D%0A%7B%7B%7B%28y-abx-a%5E2y%29%2Fx=c\"\r\n" );
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document.write( "Use this and the third original equation to substitute\r\n" );
document.write( "for both c and z in the first equation:\r\n" );
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document.write( "\"x=cy%2Bbz\"\r\n" );
document.write( "\"x=%28%28y-abx-a%5E2y%29%2Fx%29y%2Bb%28bx%2Bay%29\"\r\n" );
document.write( "Multiply thru by x:\r\n" );
document.write( "\"x%5E2=%28y-abx-a%5E2y%29y%2Bbx%28bx%2Bay%29\"\r\n" );
document.write( "\"x%5E2=y%5E2-abxy-a%5E2y%5E2%2Bb%5E2x%5E2%2Babxy\"\r\n" );
document.write( "\"x%5E2=y%5E2-cross%28abxy%29-a%5E2y%5E2%2Bb%5E2x%5E2%2Bcross%28abxy%29\"\r\n" );
document.write( "\"x%5E2=y%5E2-a%5E2y%5E2%2Bb%5E2x%5E2\"\r\n" );
document.write( "\"x%5E2-b%5E2x%5E2=y%5E2-a%5E2y%5E2\"\r\n" );
document.write( "\"x%5E2%281-b%5E2%29=y%5E2%281-a%5E2%29\"\r\n" );
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document.write( "Divide both sides by \"%281-a%5E2%29%281-b%5E2%29\"\r\n" );
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document.write( "\"x%5E2%2F%281-a%5E2%29=y%5E2%2F%281-b%5E2%29\" \r\n" );
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document.write( "To prove that one of these also equals \"z%5E2%2F%281-c%5E2%29\"\r\n" );
document.write( "is exactly similar to the above.\r\n" );
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document.write( "Edwin
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