document.write( "Question 1208230: If x^(√y) - z = 20,
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Algebra.Com's Answer #846513 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "To any/every person, having introductory mathematical level, should be clear, that this equation \r\n" );
document.write( "has infinitely many solutions in real numbers (the cardinality of the set of solution is CONTINUUM).\r\n" );
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document.write( "Therefore, in order for the problem would make sense, it is reasonable to restrict the solution set by positive integer numbers.\r\n" );
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document.write( "Then one solution is easy to guess: it is  x= 5, y= 4, z= 5.\r\n" );
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document.write( "It is not difficult to guess the second solution: x= 6, y= 4, z = 16.\r\n" );
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document.write( "Actually, this equation has infinitely many solutions even in integer numbers.\r\n" );
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document.write( "Indeed, take x arbitrary positive integer greater than or equal to 5;\r\n" );
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document.write( "        take y= 4;\r\n" );
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document.write( "        then adjust z using the formula  z =  - 20.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is continuum set of solutions in real numbers and countable set of solutions in integer numbers.\r
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