document.write( "Question 1094574: Solve for x and y if 4xy=-15 and 4x^3+4y^3=49 \n" ); document.write( "

Algebra.Com's Answer #709142 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "Solve for x and y if 4xy=-15 and 4x^3+4y^3=49
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document.write( "4xy = -15                    (1)\r\n" );
document.write( "4x^3 + 4y^3 = 49             (2)\r\n" );
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document.write( "HINT.  Use this trick:  Raise both sides of the eq(1) to degree 3.  You will get\r\n" );
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document.write( "64x^3*y^3 = -3375,           (3)\r\n" );
document.write( "4x^3 + 4y^3 = 49.            (4)\r\n" );
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document.write( "Introduce new variables  u = x^3, v = y^3.  Then the system (3),(4) takes the form\r\n" );
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document.write( "64uv = -3375,\r\n" );
document.write( "4u + 4v = 49.\r\n" );
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document.write( "In this way you reduced your quite complicated system to much more simple.\r\n" );
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document.write( "The rest is just a standard exercise in solving quadratic equation.\r\n" );
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