document.write( "Question 1208298: if (x/y) + (y/x) = 1 , then y'' = (y/x) (True or False) \n" ); document.write( "

Algebra.Com's Answer #846629 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "if (x/y) + (y/x) = 1 , then y'' = (y/x) (True or False)
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document.write( "Let's investigate which  (or what)  function y(x) can be.\r\n" );
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document.write( "We have\r\n" );
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document.write( "     +  = 1.\r\n" );
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document.write( "Let  z = .  Then\r\n" );
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document.write( "     + z = 1,\r\n" );
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document.write( "    1 + z^2 = z,\r\n" );
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document.write( "    z^2 - z + 1 = 0,\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "So,    has the constant value    or  .  Hence,\r\n" );
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document.write( "    y = z*x,  where  z is one of the two complex numbers  z =  =   or  z =  = .\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    y' = z = const  and then  y'' = 0.\r\n" );
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document.write( "Thus we have to compare, from one side,  y'' = 0  and, from the other side,   =  or ,  what are not zero.\r\n" );
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document.write( "        So, the answer to the problem's question is  .\r\n" );
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document.write( "But an interesting fact, which is worth to be noticed, is that  y' = z =   has one of the two possible constant values\r\n" );
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document.write( "  or  .\r\n" );
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