document.write( "Question 1201936: If p + 1/p = 5 and p does not equal 0, which of the following is a possible value of p - 1/p ?\r
\n" ); document.write( "\n" ); document.write( "(A) sqrt(25)
\n" ); document.write( "(B) sqrt(24)
\n" ); document.write( "(C) sqrt(23)
\n" ); document.write( "(D) sqrt(22)
\n" ); document.write( "(E) sqrt(21) \n" ); document.write( "
Algebra.Com's Answer #836516 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "If p + 1/p = 5 and p does not equal 0, which of the following is a possible value of p - 1/p ?
\n" ); document.write( "(A) sqrt(25)
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\n" ); document.write( "(C) sqrt(23)
\n" ); document.write( "(D) sqrt(22)
\n" ); document.write( "(E) sqrt(21)
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document.write( "If  \"p\" + \"1%2Fp\" = 5,  then by squaring\r\n" );
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document.write( "    p^2 + 2 + \"1%2Fp%5E2\" = 25\r\n" );
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document.write( "    p^2 + \"1%2Fp%5E2\" = 25 - 2 = 23\r\n" );
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document.write( "    p^2 - 2 + \"1%2Fp%5E2\" = 23 - 2 = 21\r\n" );
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document.write( "    \"%28p+-+1%2Fp%29%5E2\" = 21\r\n" );
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document.write( "    \"p\" - \"1%2Fp\" = +/- \"sqrt%2821%29\".\r\n" );
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document.write( "That is all that we can state about  \"p\" - \"1%2Fp\".\r\n" );
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document.write( "We can not state that it is necessary positive: it can be either positive  \"sqrt%2821%29\"  or negative  \"-sqrt%2821%29\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "You can check my solution and my statement directly.\r
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\n" ); document.write( "\n" ); document.write( "From the given equation, it implies   p^2 - 5p + 1 = 0,\r
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\n" ); document.write( "\n" ); document.write( "giving the solutions   \"p%5B1%2C2%5D\" = \"%285+%2B-+sqrt%2821%29%29%2F2\",  that are either   4.791287847  or   0.208712153.\r
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\n" ); document.write( "\n" ); document.write( "First     value gives   p - \"1%2Fp\" = 4.582575695 = \"sqrt%2821%29\".\r
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\n" ); document.write( "\n" ); document.write( "Second value gives   p - \"1%2Fp\" = -4.582575695 = \"-sqrt%2821%29\".\r
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\n" ); document.write( "\n" ); document.write( "So,  what we can state definitely,  is that  (A),  (B),  (C)  and  (D)  never may happen;\r
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\n" ); document.write( "\n" ); document.write( "of listed options,  only  (E)  may happen.\r
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\n" ); document.write( "\n" ); document.write( "But for completeness,  also   \"p\" - \"1%2Fp\" = \"-sqrt%2821%29\"  may happen,  too,  in addition to options listed in the problem's list.\r
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