document.write( "Question 1086799: If x^2 + 1/x^2 =102, find the value of x^3 - 1/x^3 \n" ); document.write( "
Algebra.Com's Answer #701038 by rothauserc(4718)\"\" \"About 
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x^2 + 1/x^2 = 102
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\n" ); document.write( "x^4 + 1 = 102x^2, for x not = 0
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\n" ); document.write( "x^4 -102X^2 +1 = 0
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\n" ); document.write( "let u = x^2, then
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\n" ); document.write( "u^2 -102u = -1
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\n" ); document.write( "complete the square
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\n" ); document.write( "u^2 -102u + 2601 = 2601 -1
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\n" ); document.write( "(u -51)^2 = 2600
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\n" ); document.write( "take square root of both sides of =
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\n" ); document.write( "u - 51 = 50.99
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\n" ); document.write( "u = 51 + 50.99 = 101.99
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\n" ); document.write( "u = x^2, then
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\n" ); document.write( "x^2 = 101.99
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\n" ); document.write( "x = + or - 10.099
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\n" ); document.write( "x^3 - 1/x^3 = ?
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\n" ); document.write( "1) (10.099)^3 - 1/(10.099)^3 = 1029.994
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\n" ); document.write( "2) (-10.099)^3 - 1/(-10.099)^3 = −1029.994
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\n" ); document.write( "check answers for x
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\n" ); document.write( "x^2 + 1/x^2 = 102
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\n" ); document.write( "(10.099)^2 + 1/(10.099)^2 = 102
\n" ); document.write( "101.999 = 102
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\n" ); document.write( "(-10.099)^2 + 1/(-10.099)^2 = 102
\n" ); document.write( "101.999 = 102
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