document.write( "Question 1035273: Solve these equations simultaneously to find a and r:
\n" ); document.write( "a(r^8 - 8r^5)=0
\n" ); document.write( "a(1-r^5)/(1-r) = 93 \n" ); document.write( "
Algebra.Com's Answer #649932 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\"system%28a%28r%5E8+-+8r%5E5%29=0%2C+a%281-r%5E5%29%2F%281-r%29+=+93%29\"
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document.write( "Factor out r³ in the first equation\r\n" );
document.write( "Multiply both sides of second equation by (1-r).\r\n" );
document.write( "[Note that r cannot equal to 1 for that would make\r\n" );
document.write( "the denominator of the original second equation 0.\r\n" );
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document.write( "\"system%28a%28r%5E3%5E%22%22%28r%5E5-8%29%29=0%2C+a%281-r%5E5%29=93%281-r%29%29\"  \r\n" );
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document.write( "Write the first equation as\r\n" );
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document.write( "\"ar%5E3%28r%5E5-8%29=0\"\r\n" );
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document.write( "Use the zero-factor principle:\r\n" );
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document.write( "Now we must find corresponding values\r\n" );
document.write( "for \"a\":\r\n" );
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document.write( "Substitute a=0 in the second equation\r\n" );
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document.write( "\"a%281-r%5E5%29=93%281-r%29\"\r\n" );
document.write( "\"0%281-r%5E5%29=93%281-r%29\" \r\n" );
document.write( "\"0=93%281-r%29\"\r\n" );
document.write( "\"0=1-r\"\r\n" );
document.write( "\"r=1\"\r\n" );
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document.write( "But we must disregard that value since it\r\n" );
document.write( "causes the denominator in the original second\r\n" );
document.write( "equation to become 0.  Therefore we must\r\n" );
document.write( "also disregard a=0.\r\n" );
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document.write( "Substitute r=0 in the second equation\r\n" );
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document.write( "\"a%281-r%5E5%29=93%281-r%29\"\r\n" );
document.write( "\"a%281-0%5E5%29=93%281-0%29\" \r\n" );
document.write( "\"a=93\"\r\n" );
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document.write( "So one solution is (a,r) = (93,0)\r\n" );
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document.write( "Substitute \"r=root%285%2C8%29\" in the second equation\r\n" );
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document.write( "\"a%281-r%5E5%29=93%281-r%29\"\r\n" );
document.write( "\"a%281-%28root%285%2C8%29%29%5E5%29=93%281-%28root%285%2C8%29%29%5E%22%22%29\" \r\n" );
document.write( "\"a%281-8%29=93%281-root%285%2C8%29%29\"\r\n" );
document.write( "\"-7a=93%281-root%285%2C8%29%29\"\r\n" );
document.write( "\"a=expr%28-93%2F7%29%281-root%285%2C8%29%29\"\r\n" );
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document.write( "Although that satisfies the second equation, we must check to\r\n" );
document.write( "see if it satisfies the first equation as well:\r\n" );
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document.write( "\"a%28r%5E8+-+8r%5E5%29=0\"\r\n" );
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document.write( "The fractional powers of 8 are irrational, so none\r\n" );
document.write( "of those factors can equal 0, so the equation cannot be true\r\n" );
document.write( "so \"r=root%285%2C8%29\" does not produce a solution.\r\n" );
document.write( "However we could not have known this without substituting\r\n" );
document.write( "in the first equation.\r\n" );
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document.write( "There is but one solution: (a,r) = (93,0)\r\n" );
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document.write( "Edwin
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