Question

pls help in solving this problem

Answer 1

GIVEN
x + (1 / X) = 3
SQUARING BOTH SIDES
x^2 + 2 + ( 1 / x^2) = 9
x^2 + (1/ x^2) = 9 - 2
x^2 + (1/ x^2) = 7 - - - - - - - - - - (1)

To find
x^6 + (1 / x^6)

CUBING BOTH SIDE
[x^2 + (1/ x^2)]^3 = (7) ^3

FORMULA
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Therefore,
x^6 + (3x^4 / x^2) + 3x^2 / x^4 + 1 / x^6 = 343
x^6 + 1 / x^6 =
- [(3x^4 / x^2) + (3x^2 / x^4)] + 343
= - 3x^2 - (3 / x^2) + 343
= - 3[x^2 + (1 / x^2)] + 343- - - - (2)

SUBSITUTE (1) in (2)
x^6 + 1 / x^6 = - 3 (7) + 343
= - 21 + 343
= 322