document.write( "Question 1209394: Let x and y be complex numbers. If x + y = 2 and xy = 7 - x^2 - y^2, then what is x^2 + y^2? \n" ); document.write( "

Algebra.Com's Answer #848742 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Let x and y be complex numbers. If x + y = 2 and xy = 7 - x^2 - y^2, then what is x^2 + y^2?
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document.write( "x^2 + y^2 = add and subtract 2xy = (x^2 + 2xy + y^2) - 2xy = first parentheses is the square = (x+y)^2 - 2xy = \r\n" );
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document.write( "          = substitute the given values = 2^2 - 2*(7-x^2-y^2).\r\n" );
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document.write( "Thus you have now\r\n" );
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document.write( "    x^2 + y^2 = 4 - 14 + 2(x^2 + y^2),\r\n" );
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document.write( "    x^2 + y^2 = -10 + 2(x^2 + y^2),\r\n" );
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document.write( "     10 = x^2 + y^2.\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "ANSWER.  x^2 + y^2 = 10.\r\n" );
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