document.write( "Question 994117: Please help me solve this question\r
\n" ); document.write( "\n" ); document.write( "If x2 - 2y2 = 7 and xy = 3 , find x and y\r
\n" ); document.write( "\n" ); document.write( "Note : the number 2 behind x and 2y means squared \r
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Algebra.Com's Answer #613332 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( " $\"system%28x%5E2+-+2y%5E2+=+7%2C%0D%0Axy+=+3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Express y from the second equation, y = $\"3%2Fx\"$ , and substitute it into the first equation. You will get single equation for the unknown x:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2\"$ - $\"2%283%2Fx%29%5E2\"$ = $\"7\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Multiply both sides by $\"x%5E2\"$ . You will get\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E4+-+7x%5E2+-+18\"$ = $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Factor:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B2%29%2A%28x%5E2-9%29\"$ = $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The roots are $\"x%5E2\"$ = - $\"2\"$ and $\"x%5E2\"$ = $\"9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The real roots are x = +/- 3.\r
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\n" ); document.write( "\n" ); document.write( "Correspondingly y = +/- 1.\r
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\n" ); document.write( "\n" ); document.write( "Answer. The pairs (x,y) = (3,1) and (x,y) = (-3,-1) are real solutions.\r
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