document.write( "Question 877324: Find a real root of the equation x3 - 3x +1 =0
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Algebra.Com's Answer #529293 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x³-3x+1 = 0\r\n" );
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document.write( "Try substituting x=0 to see if we get close to 0\r\n" );
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document.write( "0³-3·0+1 = 1\r\n" );
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document.write( "x=0 gives 1, too big\r\n" );
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document.write( "Try 1\r\n" );
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document.write( "1³-3·2+1 \r\n" );
document.write( "       -1\r\n" );
document.write( "x=1 gives -1, too small\r\n" );
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document.write( "Try something in between 0 and 1\r\n" );
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document.write( "Try .5\r\n" );
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document.write( ".5³-3·(.5)+1 = -.375 \r\n" );
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document.write( "x=-.375 is closer to 0, but still too small\r\n" );
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document.write( "So we try something in between 0 and .5, closer to .5, \r\n" );
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document.write( "Try .3\r\n" );
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document.write( ".3³-3·(.3)+1 = .127 \r\n" );
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document.write( ".127 is closer to 0, but it's too big\r\n" );
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document.write( "So we try something in between .3 and .5, closer to .3\r\n" );
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document.write( "Try .35\r\n" );
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document.write( ".35³-3·(.35)+1 = -.007125 \r\n" );
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document.write( "Nope, that's closer to 0, but it's too small\r\n" );
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document.write( "So we try something in between .3 and .35, closer to .35\r\n" );
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document.write( "Try .345\r\n" );
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document.write( ".345³-3·(.345)+1 = .006063635        \r\n" );
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document.write( "Nope, that's closer to 0, but it's too big\r\n" );
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document.write( "So we try something in between .345 and .35,\r\n" );
document.write( "closer to .345, \r\n" );
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document.write( "Try .347\r\n" );
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document.write( ".347³-3·(.347)+1 = .00078192 \r\n" );
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document.write( "Nope, closer to 0, but still too big\r\n" );
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document.write( "So we try something in between .347 and .35,\r\n" );
document.write( "closer to .347\r\n" );
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document.write( "Try .348\r\n" );
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document.write( ".348³-3·(.348)+1 = .0018558 \r\n" );
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document.write( "Nope, not closer to 0, still too big\r\n" );
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document.write( "So we try something in between .347 and .38,\r\n" );
document.write( "closer to .347\r\n" );
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document.write( "Try .3472\r\n" );
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document.write( ".3472³-3·(.3472)+1 = .00025421 \r\n" );
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document.write( "Nope, closer to 0, still too big\r\n" );
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document.write( "So we try something in between .3472 and .345,\r\n" );
document.write( "but much closer to .3472 since .00025421 is much\r\n" );
document.write( "closer to 0 than -.007125.\r\n" );
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document.write( "So try .3473 \r\n" );
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document.write( ".3473³-3·(.3473)+1 = -.000009615\r\n" );
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document.write( "That's a lot closer to 0 than when we tried .3472\r\n" );
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document.write( "So we choose something much closer to .3473 than to .3472.\r\n" );
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document.write( "Se we can stop there.\r\n" );
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document.write( "To four decimal places, it's .3473\r\n" );
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document.write( "Edwin
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