Question

If x+ 1/x =2, then x³ + 1/x³ =
A. 64
B. 14
C. 8
D. 2

Answer 1

Given : x + 1/x = 2

 

To find : value of  x³ + 1/x³

 

Solution :  

We have   x + 1/x = 2 ……..(1)

On cubing eq 1 both sides,  

(x + 1/x)³   = 2³

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

x³ +1/x³ + 3 x × 1/x (x + 1/x) = 8

x³ + 1/x³ + 3 (x + 1/x) = 8

x³ + 1/x³ + 3 (2) = 8

 x³ + 1/x³ + 6 = 8

x³ + 1/x³ = 8 - 6

x³ + 1/x³ = 2

Hence the value of  x³ + 1/x³ is  2.

Among the given options option (D) 2 is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Given:

x + 1/x = 2

To find:

x³ + 1/x³ = ?

Solution:

Identity to be used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Here, we take:

a = x

b = 1/x

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

=> 2³ = x³ + 1/x³ + 3(2)

=> x³ + 1/x³ = 8 - 6

=> x³ + 1/x³ = 2

Thus, option (D) 2 is right.