Answer:
52
Explanation:
(x+1/x)² -2 = 14
(x+1/x)²= 16
x+1/x = √ 16 =4
∴ x+1/x = 4
(x+1/x)³= x³ + 1/x³ + 3 × x × 1/x (x + 1/x) (cubic Identity)
(x+1/x)³ = x³ +1/x³+ 3(4)
(4)³=x³+1/x³+12
64-12=x³+1/x³
x² + 1/x² = 14
(x + 1/x)² -2.x.1/x = 14
(x + 1/x )² -2 = 14
(x + 1/x )² = 16
take square root both sides
(x + 1/x) = 4
then,
[a³+b³=(a+b)³-3ab(a+b)]
x³ + 1/x³ = ( x + 1/x)³ - 3.x.1/x(x + 1/x)
= ( x +1/x)³ -3(x + 1/x)
= (4)³ -3(4)
= 64 - 12
= 52
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