document.write( "Question 644404: a³+b³=72, a²-b²=12
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Algebra.Com's Answer #405026 by Edwin McCravy(20055)\"\" \"About 
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a³+b³=72, a²-b²=12
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document.write( "(1)     a³+b³ = 72\r\n" );
document.write( "(2)     a²-b² = 12\r\n" );
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document.write( "From (2)   b² = a²-12\r\n" );
document.write( "(3)         b = ±Öa²-12\r\n" );
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document.write( "Substituting the negative solution in (1) and simplifying\r\n" );
document.write( "gives a 6th degree equation with only imaginary solutions.\r\n" );
document.write( "I will not deal with the imaginary solutions. So we will\r\n" );
document.write( "only consider\r\n" );
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document.write( "(3)         b = Öa²-12\r\n" );
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document.write( "Substituting this positive square root and simplifying gives\r\n" );
document.write( "this: \r\n" );
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document.write( "   a4 - 4a3 - 12a2 + 192 = 0\r\n" );
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document.write( "which factors as\r\n" );
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document.write( " (a-4)(a3-12a-48) = 0\r\n" );
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document.write( "This has rational solution a=4.  It also has one irrational\r\n" );
document.write( "real solution and two imaginary solutions.  Substituting a=4\r\n" );
document.write( "this in (3) gives b=2\r\n" );
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document.write( "Real rational solution:  a=4, b=2\r\n" );
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document.write( "I will not deal with the irrational real solution or the imaginary \r\n" );
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document.write( "Edwin
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