document.write( "Question 48192: Checking my math on this one, we're working on Quadratics this week:\r
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Algebra.Com's Answer #31895 by atif.muhammad(135) $\"\"$ $\"About$

You can put this solution on YOUR website!

Find two positive real numbers that differ by 1 and have a product of 1\r\n" );
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document.write( "Let one of the real number be x and the other be y.\r\n" );
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document.write( "Both differ by 1: y-x = 1\r\n" );
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document.write( "Both have a product of 1 : xy = 1\r\n" );
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document.write( "We have a pair of simultaneous equations\r\n" );
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document.write( "y-x = 1....(1)\r\n" );
document.write( "xy = 1....(2)\r\n" );
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document.write( "Manipulate (1):\r\n" );
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document.write( "y-x = 1\r\n" );
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document.write( "y = (x+1)....(3)\r\n" );
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document.write( "Substitute (3) into (2):\r\n" );
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document.write( "xy = 1\r\n" );
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document.write( "x(x+1) = 1\r\n" );
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document.write( "x^2 + x = 1\r\n" );
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document.write( "x^2 + x -1 = 0  ---- Oooo...a quadratic equation!\r\n" );
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document.write( "I'm not going to bother factorising it as I remember the answer to this equation. It gives a golden ratio as its' answer -- something like 0.618.\r\n" );
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document.write( "So if x = something like 0.618\r\n" );
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document.write( "Then y = x + 1 = something like 1.618\r\n" );
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document.write( "Hope that helps!\r\n" );
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