Question

If x- 1/x= 7, find the value of x³ - 1/x³

Answer 1

Given : x - 1/x = 7

 

To find : value of x³ - 1/x³

 

Solution :  

We have x - 1/x = 7 ……..(1)

On cubing eq 1 both sides,  

(x - 1/x)³ = (7)³

By using the identity, (a - b)³ = a³ - b³ - 3ab(a - b)  

x³ - 1/x³ - 3 x × 1/x (x - 1/x) = 343

x³ - 1/x³ - 3 (x - 1/x) = 343

x³ - 1/x³ - 3 (7) = 343

x³ - 1/x³ - 21 = 343

x³ - 1/x³  = 343 + 21

x³ - 1/x³ = 364

Hence the value of  x³ - 1/x³  is 364 .

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Answer: 364

Solution:

x - 1/x = 7

For Cubing both the sides, use the identity:

(a - b)³ = a³ + b³ - 3ab(a + b)

So,

(x - 1/x)³ = 7³

x³ - 1/x³ + 3x × 1/x (x + 1/x) = 343

x³ - 1/x³ + 3(x + 1/x) = 343

x³ - 1/x³ + 3 × 7 = 343

x³ - 1/x³ = 343 + 21

x³ + 1/x³ = 364