document.write( "Question 933335: If a,b,c, are in G.P and a^x=b^y=c^z the x,y,z are in\r
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Algebra.Com's Answer #567104 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"a%5Ex=b%5Ey=c%5Ez\"\r\n" );
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document.write( "since a,b,c are in GP, their common ratio is \"b%2Fa\".  Therefore \"c=b%2A%28b%2Fa%29=%28b%5E2%29%2Fa=a%5E%28-1%29b%5E2\"\r\n" );
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document.write( "\"a%5Ex=b%5Ey=%28a%5E%28-1%29b%5E2%29%5Ez\"\r\n" );
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document.write( "Raise all three parts to the \"1%2F%28xyz%29\" power\r\n" );
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document.write( "Multiply exponents:\r\n" );
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document.write( "(1)   \r\n" );
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document.write( "From the first two expressions of (1)\r\n" );
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document.write( "Raise both sides to the z power\r\n" );
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document.write( "(2)  \r\n" );
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document.write( "From the first and third expressions of (1)\r\n" );
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document.write( "Raise both sides to the y power:\r\n" );
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document.write( "Multiply both sides by \"matrix%282%2C1%2C%22%22%2Ca%5E%281%2Fx%29%29\":\r\n" );
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document.write( "(3)  \r\n" );
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document.write( "Square both sides of (2)\r\n" );
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document.write( "Substitute \"matrix%282%2C1%2C%22%22%2Ca%5E%282%2Fy%29%29\" for \"matrix%282%2C1%2C%22%22%2Cb%5E%282%2Fx%29%29\" in (3)   \r\n" );
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document.write( "(3)  \r\n" );
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document.write( "Equate exponents of a in (3)\r\n" );
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document.write( "\"1%2Fz%2B1%2Fx=2%2Fy\"\r\n" );
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document.write( "\"1%2Fz%2B1%2Fx=1%2Fy%2B1%2Fy\"\r\n" );
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document.write( "\"1%2Fz-1%2Fy=1%2Fy-1%2Fx+=+matrix%281%2C2%2Ccommon%2Cdifference%29\"\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "\"matrix%281%2C8%2C%0D%0A%0D%0Ax%2C++%22%2C%22%2C++y%2C+%22%2C%22%2C++z%2C++are%2C+in%2C+HP%29\"\r\n" );
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document.write( "Edwin
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