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24 votes
If x + 1/x = 5, find the value of x^3 + 1/x^3

User Mathetes
by
4.8k points

2 Answers

9 votes

Answer:

110

Explanation:

The expansion (a + b)³ is

(a + b)³ = a³ + b³ + 3ab(a + b)

Then

(x +
(1)/(x) )³ with a = x and b =
(1)/(x)

= x³ +
(1)/(x^3) + 3x .
(1)/(x) (x +
(1)/(x) )

Thus

x³ +
(1)/(x^3) = (x +
(1)/(x) )³ - 3(x +
(1)/(x) )

= 5³ - 3(5)

= 125 - 15

= 110

User Ruivo
by
5.5k points
9 votes

Answer:

x=5/3 your answer right answer

User Duggulous
by
5.6k points