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)![]() ![]() You can put this solution on YOUR website! x^2 + 1/x^2 = 102 \n" ); document.write( ": \n" ); document.write( "x^4 + 1 = 102x^2, for x not = 0 \n" ); document.write( ": \n" ); document.write( "x^4 -102X^2 +1 = 0 \n" ); document.write( ": \n" ); document.write( "let u = x^2, then \n" ); document.write( ": \n" ); document.write( "u^2 -102u = -1 \n" ); document.write( ": \n" ); document.write( "complete the square \n" ); document.write( ": \n" ); document.write( "u^2 -102u + 2601 = 2601 -1 \n" ); document.write( ": \n" ); document.write( "(u -51)^2 = 2600 \n" ); document.write( ": \n" ); document.write( "take square root of both sides of = \n" ); document.write( ": \n" ); document.write( "u - 51 = 50.99 \n" ); document.write( ": \n" ); document.write( "u = 51 + 50.99 = 101.99 \n" ); document.write( ": \n" ); document.write( "u = x^2, then \n" ); document.write( ": \n" ); document.write( "x^2 = 101.99 \n" ); document.write( ": \n" ); document.write( "x = + or - 10.099 \n" ); document.write( ": \n" ); document.write( "****************************************** \n" ); document.write( "x^3 - 1/x^3 = ? \n" ); document.write( ": \n" ); document.write( "1) (10.099)^3 - 1/(10.099)^3 = 1029.994 \n" ); document.write( ": \n" ); document.write( "2) (-10.099)^3 - 1/(-10.099)^3 = −1029.994 \n" ); document.write( ": \n" ); document.write( "check answers for x \n" ); document.write( ": \n" ); document.write( "x^2 + 1/x^2 = 102 \n" ); document.write( ": \n" ); document.write( "(10.099)^2 + 1/(10.099)^2 = 102 \n" ); document.write( "101.999 = 102 \n" ); document.write( ": \n" ); document.write( "(-10.099)^2 + 1/(-10.099)^2 = 102 \n" ); document.write( "101.999 = 102 \n" ); document.write( ": \n" ); document.write( "our answer checks \n" ); document.write( "******************************************* \n" ); document.write( ":\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |