document.write( "Question 1207659: Find the real solutions of the equation. \r
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\n" ); document.write( "\n" ); document.write( "This one threw me into a loop.\r
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\n" ); document.write( "\n" ); document.write( "4x^(1/2) - 9x^(1/4) + 4 = 0 \n" ); document.write( "
Algebra.Com's Answer #845656 by ikleyn(52784)\"\" \"About 
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document.write( "Introduce new variable  y = x^(1/4).\r\n" );
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document.write( "Then our original equation takes the form\r\n" );
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document.write( "    4y^2 - 9y + 4 = 0.\r\n" );
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document.write( "It is a quadratic equation for y.  Solve it using the quadratic formula\r\n" );
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document.write( "    \"y%5B1%2C2%5D\" = \"%289+%2B-+sqrt%28%28-9%29%5E2+-+4%2A4%2A4%29%29%2F%282%2A4%29\" = \"%289+%2B-+sqrt%2881-64%29%29%2F8\" = \"%289+%2B-+sqrt%2817%29%29%2F8\".\r\n" );
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document.write( "Thus, there are two real roots for y:  y= \"%289+%2B+sqrt%2817%29%29%2F8\"  and  y= \"%289+-+sqrt%2817%29%29%2F8\".\r\n" );
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document.write( "It gives two real positive solutions for x\r\n" );
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document.write( "    x = y^4 = \"%28%289+%2B+sqrt%2817%29%29%2F8%29%5E4\" = 7.240799963  (approximately).\r\n" );
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document.write( "and\r\n" );
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document.write( "    x = y^4 = \"%28%289+-+sqrt%2817%29%29%2F8%29%5E4\" = 0.138106287  (approximately).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Again, the method of solution is changing the variable.\r
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