document.write( "Question 1105658: One pair of integers (x,y) solves \"sqrt%284sqrt%287%29+%2B+11%29+=+y+%2B+sqrt%28x%29\". Find x.y \n" ); document.write( "
Algebra.Com's Answer #720520 by Edwin McCravy(20067)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sqrt%284sqrt%287%29+%2B+11%29+=+y+%2B+sqrt%28x%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%284sqrt%287%29+%2B+11%29%29%5E2+=+%28y+%2B+sqrt%28x%29%29%5E2\"\r\n" );
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document.write( "\"4sqrt%287%29+%2B+11+=+%28y+%2B+sqrt%28x%29%29%28y+%2B+sqrt%28x%29%29\"\r\n" );
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document.write( "\"FOIL\" out the right side:\r\n" );
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document.write( "\"4sqrt%287%29+%2B+11+=+y%5E2+%2B+y%2Asqrt%28x%29%2By%2Asqrt%28x%29%2B%28sqrt%28x%29%29%5E2\"\r\n" );
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document.write( "\"4sqrt%287%29+%2B+11+=+y%5E2+%2B+2y%2Asqrt%28x%29%2Bx\"\r\n" );
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document.write( "Since we know that one pair of integers (x,y) solves it,\r\n" );
document.write( "the terms with the square roots on each side must be equal, \r\n" );
document.write( "and therefore the terms without square roots must also be equal.\r\n" );
document.write( "So we have this system of equations\r\n" );
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document.write( "\"system%284sqrt%287%29=2y%2Asqrt%28x%29%2C11=y%5E2%2Bx%29\"\r\n" );
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document.write( "I'll let you finish.  \r\n" );
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document.write( "Divide both sides of the first equation\r\n" );
document.write( "by 2, then square both sides.\r\n" );
document.write( "Solve it for either x or y2\r\n" );
document.write( "Substitute what you get into the second equation  \r\n" );
document.write( "Solve for that letter.\r\n" );
document.write( "Substitute to find the other letter.\r\n" );
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document.write( "Edwin
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