document.write( "Question 1111874: If x+y=1 and $\"x%5E3%2By%5E3=19\"$ , find the value of $\"x%5E2%2By%5E2\"$ \n" ); document.write( "

Algebra.Com's Answer #726910 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Let me show you the RIGHT WAY solving this problem.\r
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document.write( "We are given\r\n" );
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document.write( "x + y = 1.\r\n" );
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document.write( "Cube both sides. You will get\r\n" );
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document.write( "1 =  =  + .\r\n" );
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document.write( "Now replace  by 19 ( ! given !)  and replace (x+y) by 1 in the right side.  You will get\r\n" );
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document.write( "1 = 19 + 3xy,    which implies  3xy = 1 - 19 = -18.\r\n" );
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document.write( "Hence, xy =  = -6.\r\n" );
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document.write( "Now the last step is \r\n" );
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document.write( " =  = 1 - 2xy = 1 - 2*(-6) = 1 + 12 = 13.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer.   x^2 + y^2 = 13.\r
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\n" ); document.write( "\n" ); document.write( "            It is how this problem MUST be solved, and it is how IT IS EXPECTED you will solve it   (if you know the way !)\r
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\n" ); document.write( "\n" ); document.write( "            Any other way is the way to N O W H E R E.\r
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems, look into the lesson\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate expressions involving $\"%28x+%2B+1%2Fx%29\"$ , $\"%28x%5E2%2B1%2Fx%5E2%29\"$ , $\"%28x%5E3+%2B+1%2Fx%5E3%29\"$ and $\"%28x%5E5%2B1%2Fx%5E5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "in this site.\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 lesson is 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
\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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\n" ); document.write( "\n" ); document.write( "Again:   This problem is to check your competency: whether you know the way . . . \r
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\n" ); document.write( "\n" ); document.write( "             It is very good for an interview . . . (on a mathematical position . . . )\r
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