document.write( "Question 1118300: If x +1/x= 6, find the value of x^2 +1/x^2 \n" ); document.write( "
Algebra.Com's Answer #733584 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!
Ans: \"+highlight%28+34+%29+\"\r
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\n" ); document.write( "\n" ); document.write( "Its just a small amount of algebra and rationalization of fractions.\r
\n" ); document.write( "\n" ); document.write( "\"+x+%2B+1%2Fx+=+6+\"
\n" ); document.write( "\"++x%5E2-6x++=+-1+\"
\n" ); document.write( "\"++x%5E2-6x%2B9+=+-1+%2B+9+\"
\n" ); document.write( "\"++%28x-3%29%5E2+=+8+\"
\n" ); document.write( "\"++%28x-3%29+=+%2B-sqrt%288%29+\" (*)
\n" ); document.write( " \"+blue%28+x+=+3%2Bsqrt%288%29+%29+\"
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\n" ); document.write( "\n" ); document.write( "Considering \"+x=3%2Bsqrt%288%29+\":
\n" ); document.write( "Now plug in this value of x into \"+x%5E2+%2B+1%2Fx%5E2+\":
\n" ); document.write( " \"+%283+%2B+sqrt%288%29%29%5E2+=+9%2B6%2A%28sqrt%288%29%29%2B8+=+17%2B6sqrt%288%29+\"\r
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\n" ); document.write( "(*) Also, \"+3-sqrt%288%29+\" solves x + 1/x = 6 so that number must be plugged into x^2 + 1/x^2 to get a 2nd answer. But that answer will also be \"+highlight%2834%29+\" \r
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\n" ); document.write( "Good solution @MathTherapy! \n" ); document.write( "
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