document.write( "Question 1092216: If a+1/a=7 find the value of \r
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Algebra.Com's Answer #706815 by ikleyn(52909)\"\" \"About 
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\n" ); document.write( "If a+1/a=7 find the value of (a-1/a)^2 and a^4+1/a^4
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document.write( "1.  \"a%2B1%2Fa\" = 7  ====>  square both sides  ====>\r\n" );
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document.write( "    \"a%5E2\" + \"2%2Aa%2A%281%2Fa%29\" + \"1%2Fa%5E2\" = 49  ====>  notice that \"a%2A%281%2Fa%29\" = 1  ====>\r\n" );
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document.write( "    \"a%5E2\" + 2 + \"1%2Fa%5E2\" = 49  ====>  \"a%5E2\" + \"1%2Fa%5E2\" = 49 - 2  ====>  \"a%5E2\" + \"1%2Fa%5E2\" = 47  ====>\r\n" );
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document.write( "    \"a%5E2\" - 2 + \"1%2Fa%5E2\" = 47 - 2 = 45  ====>  \"%28a+-+1%2Fa%29%5E2\" = 45\r\n" );
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document.write( "2.  Notice that in the part \"1\" we just deduced as an intermediate result that\r\n" );
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document.write( "    if  \"a%2B1%2Fa\" = 7  then  \"a%5E2\" + \"1%2Fa%5E2\" = 47.\r\n" );
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document.write( "    Square the last equality one more time. You will get\r\n" );
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document.write( "    \"a%5E4\" + \"2%2Aa%5E2%2A%281%2Fa%5E2%29\" + \"a%5E4\" = \"47%5E2\"  ====>\r\n" );
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document.write( "    \"a%5E4\" + 2 + \"1%2Fa%5E4\" = \"47%5E2\"  ====>\r\n" );
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document.write( "    \"a%5E4\" + \"1%2Fa%5E4\" = \"47%5E2-2\" = 2207.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer.  If  \"a%2B1%2Fa\" = 7  then  \"%28a+-+1%2Fa%29%5E2\" = 45  and  \"a%5E4\" + \"1%2Fa%5E4\" = 2207.\r
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\n" ); document.write( "See the lesson \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate expressions involving  \"%28x+%2B+1%2Fx%29\",  \"%28x%5E2%2B1%2Fx%5E2%29\"  and  \"%28x%5E3%2B1%2Fx%5E3%29\"\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Evaluation, substitution\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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