Question

If x+ 1/x =3, then x⁶ + 1/x⁶ =
A. 927
B. 414
C. 364
D. 322

Answer 1

Given : x + 1/x = 3

To find : value of  x⁶ + 1/x⁶

 Solution :  

We have x + 1/x = 3 ……..(1)

On squaring eq 1 both sides :

(x + 1/x)²   = 3²

By Using Identity : (a + b)²  = a² + b² + 2ab

x² + 1/x² + 2 x × 1/x = 9

x² + 1/x² + 2 = 9

 x² + 1/x² = 9 - 2

x² + 1/x² = 7 ………(2)

On Cubing eq 2 both sides :

(x² + 1/x² )³ = 7³

By Using Identity : (a + b)³  = a³ + b³ + 3ab(a + b)

(x²)³ + (1/x²)³ + 3 × x² × 1/x² (x² + 1/x²) = 343

x⁶ + 1/x⁶ + 3(x² + 1/x²) = 343

x⁶ + 1/x⁶ + 3(7) = 343

[From eq 2]

x⁶ + 1/x⁶ + 21 = 343

x⁶ + 1/x⁶  = 343 - 21

x⁶ + 1/x⁶ = 322

Hence the value of x⁶ + 1/x⁶ is 322.

Among the given options option (D) 322 is correct.

 

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Refer to the attachment.

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