document.write( "Question 1046716: Kindly help me solving it
\n" ); document.write( "By solving equation \"%281%2Bx%29%5E%282%2F3%29%2B%281-x%29%5E%282%2F3%29=4+%281-x%5E2%29%5E%281%2F3%29\" the values of x are?
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Algebra.Com's Answer #662210 by ikleyn(52835)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Kindly help me solving it
\n" ); document.write( "By solving equation \"%281%2Bx%29%5E%282%2F3%29%2B%281-x%29%5E%282%2F3%29=4+%281-x%5E2%29%5E%281%2F3%29\" the values of x are?
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document.write( "\"%281%2Bx%29%5E%282%2F3%29%2B%281-x%29%5E%282%2F3%29\" = \"4%2A%281-x%5E2%29%5E%281%2F3%29\".     (1)\r\n" );
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document.write( "Let us introduce new variables  a = \"%281%2Bx%29%5E%281%2F3%29\",  b = \"%281-x%29%5E%281%2F3%29\".  Then the equation (1) takes the form\r\n" );
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document.write( "\"a%5E2+%2B+b%5E2\" = \"4ab\".                           (2)\r\n" );
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document.write( "Divide both sides of (2) by \"b%5E2\". You will get\r\n" );
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document.write( "\"%28a%2Fb%29%5E2+%2B+1\" = \"4%2A%28a%2Fb%29\".                        (3)\r\n" );
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document.write( "Let us introduce new variable z = \"a%2Fb\".  Then the equation (3) takes the form\r\n" );
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document.write( "\"z%5E2+%2B+1\" = 4z,   or\r\n" );
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document.write( "\"z%5E2+-4z+%2B+1\" = \"0\".\r\n" );
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document.write( "Solve it by using the quadratic formula. You will get\r\n" );
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document.write( "\"z%5B1%2C2%5D\" = \"%284+%2B-+sqrt%2816-4%29%29%2F2\" = \"2+%2B-+sqrt%283%29\".\r\n" );
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document.write( "Now you come to the equations  for x:\r\n" );
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document.write( "\"%281%2Bx%29%2F%281-x%29\" = \"%282+%2B+sqrt%283%29%29%5E3\"  and/or  \r\n" );
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document.write( "\"%281%2Bx%29%2F%281-x%29\" = \"%282+-+sqrt%283%29%29%5E3\".\r\n" );
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document.write( "It is just a technique to solve them.\r\n" );
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document.write( "I think it will not be difficult for the person who comes with such a request.\r\n" );
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