document.write( "Question 1133481: Find the value of x^4+1/x^4 when x+1/x=2.Show solution without calculator
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Algebra.Com's Answer #750710 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The easiest way is just to solve \"x%2B1%2Fx=2\" for x\r\n" );
document.write( "and substitute in \"x%5E4%2B1%2Fx%5E4\"\r\n" );
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document.write( "\"x%2B1%2Fx=2\"\r\n" );
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document.write( "Multiply through by x\r\n" );
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document.write( "\"x%5E2%2Bx%2Fx=2x\"\r\n" );
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document.write( "\"x%5E2%2B1=2x\"\r\n" );
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document.write( "\"x%5E2-2x%2B1=0\"\r\n" );
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document.write( "\"%28x-1%29%28x-1%29=0\"\r\n" );
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document.write( "\"x-1=0\"\r\n" );
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document.write( "\"x=1\"\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "\"x%5E4%2B1%5E%22%22%2Fx%5E4\"\r\n" );
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document.write( "\"1%2B1%5E%22%22%2F1\"\r\n" );
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document.write( "\"1%2B1\"\r\n" );
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document.write( "\"2\"\r\n" );
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document.write( "--------------------------\r\n" );
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document.write( "But maybe you meant \"without solving for x\". If so, then:\r\n" );
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document.write( "\"x%2B1%2Fx=2\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28x%2B1%2Fx%29%5E2=2%5E2\"\r\n" );
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document.write( "\"x%5E2%2B2%28x%29%281%2Fx%5E%22%22%29%2B1%2Fx%5E2=4\"\r\n" );
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document.write( "\"x%5E2%2B2%2B1%2Fx%5E2=4\"\r\n" );
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document.write( "\"x%5E2%2B1%2Fx%5E2=2\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28x%5E2%2B1%2Fx%5E2%29%5E2=2%5E2\"\r\n" );
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document.write( "\"x%5E4%2B2%28x%5E2%29%281%2Fx%5E2%29%2B1%2Fx%5E4=4\"\r\n" );
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document.write( "\"x%5E4%2B2%2B1%2Fx%5E4=4\"\r\n" );
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document.write( "\"x%5E4%2B1%2Fx%5E4=2\"\r\n" );
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document.write( "That was done without solving for x.\r\n" );
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document.write( "Edwin
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