document.write( "Question 169252: I solved 48 problems but this one has me stumped and I have been working on it for 2hrs.
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\n" ); document.write( "x^2 + y^2 = 3
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Algebra.Com's Answer #124807 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
I solved 48 problems but this one has me stumped and I have been working on it for 2hrs.
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document.write( "\"system%28x%5E2+%2B+y%5E2+=+3%2Cx%5E2+%2B+y+=+0%29\"\r\n" );
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document.write( "Solve the second for y:\r\n" );
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document.write( "\"x%5E2%2By=0\"\r\n" );
document.write( "\"y=-x%5E2\"\r\n" );
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document.write( "Substitute in the first original equation:\r\n" );
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document.write( "\"x%5E2%2By%5E2=3\"\r\n" );
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document.write( "\"x%5E2%2B%28-x%5E2%29%5E2=3\"\r\n" );
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document.write( "\"x%5E2%2B%28x%5E4%29=3\"\r\n" );
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document.write( "\"x%5E4%2Bx%5E2-3=0\"\r\n" );
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document.write( "Let \"x%5E2=W\".  Then \"x%5E4=W%5E2\"\r\n" );
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document.write( "Substitute those:\r\n" );
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document.write( "\"W%5E2%2BW-3=0\"\r\n" );
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document.write( "This does not factor so we have to use\r\n" );
document.write( "the quadratic formula:\r\n" );
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document.write( "\"W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "where \"matrix%281%2C5%2C+++a=1%2C+%22%2C%22%2C+b=1%2C+%22%2C%22%2C+c=-3%29\"\r\n" );
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document.write( "\"W+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%2A%281%29%2A%28-3%29+%29%29%2F%282%2A%281%29%29+\" \r\n" );
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document.write( "\"W+=+%28-1+%2B-+sqrt%281%2B12%29%29%2F2+\"\r\n" );
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document.write( "\"W+=+%28-1+%2B-+sqrt%2813%29%29%2F2+\"\r\n" );
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document.write( "But we do not want W.  We want x, so\r\n" );
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document.write( "since we let \"x%5E2=W\", we have\r\n" );
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document.write( "\"x%5E2+=+%28-1+%2B-+sqrt%2813%29%29%2F2+\"  \r\n" );
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document.write( "Using the +, and the principle of\r\n" );
document.write( "square roots:\r\n" );
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document.write( "\"x+=+%22%22%2B-sqrt%28%28-1+%2B+sqrt%2813%29%29%2F2%29\" = ±\"1.141391974\", approximately\r\n" );
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document.write( "Substituting in \"y=-x%5E2\"\r\n" );
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document.write( "\"y=-x%5E2\"\r\n" );
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document.write( "\"y+=+-%28-1+%2B+sqrt%2813%29%29%2F2%29+=+-1.302775638\", approximately.\r\n" );
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document.write( "So we have two solutions:\r\n" );
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document.write( "(x, y) = (±1.141391974, -1.302775638)\r\n" );
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document.write( "Those are the only real solutions.  \r\n" );
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document.write( "To find the imaginary solutions,\r\n" );
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document.write( "we use the -, and the principle of\r\n" );
document.write( "square roots:\r\n" );
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document.write( "\"x+=+%22%22%2B-sqrt%28+%28-1+-+sqrt%2813%29%29%2F2+%29++\"= ±\"i%2Asqrt%28++%281%2Bsqrt%2813%29%29%2F2+%29\"= ±1.517489914i, approximately.\r\n" );
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document.write( "Substituting in \"y=-x%5E2\"\r\n" );
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document.write( "\"y=-x%5E2\"\r\n" );
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document.write( "\"y+=+-%28-1+-+sqrt%2813%29%29%2F2%29+=+%281%2Bsqrt%2813%29%29%2F2=+2.302775638\", approximately.\r\n" );
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document.write( "So we have two imaginary solutions:\r\n" );
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document.write( "(x,y) = (±1.517489914i,2.302775638)\r\n" );
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document.write( "Edwin
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