Question

x^4+1/x^4=36 then x^3+1/x^3=?

Answer 1

hey dear



here is your answer


Solution



Given =( x ^4 + 1 / x^4) =36


(x^4 + 1 / x^4) +2 =36



x^4 +1 / x ^4 = 36 +2


x^4 + 1 / x ^4. =38


(x^2)^2 + 1 / (x^2)^2. + 2x^2 * 1 / x^2 = 38



= ( x^2 + 1/ x^2 )^2 = √38 approx = 6.1


( x^2 + 1/ x^2 ) = 6. ( we take 6 for easy way)



Now subtracting two from both the sides we get


( x^2 - 1 / x ^2 ) -2 = 6 -2


x^2 + 1 / x^2. - 2x * 1/x = 4


( x - 1 / x) ^2. = √4


(x - 1 / x) = 2




Cubing on both the sides we get


( x - 1/x )^3 = ( 2)^3



x^3 - 1/ x ^3 -3 *x * 1/x ( x -1 / x) = 8


x^3 - 1/x ^3 - 3( 3) = 8


(x^3 - 1/x^3 ) -9 =8


x^3 - 1/ x^3 = 9 +8


x ^3 - 1 /x^3 = 17



hence ( x^3 -1 /x^3 = 17 )



hope it helps


thank you