Question

lf x-1/x=6,find x²+1/x²​

Answer 1

Answer:

34

Step-by-step explanation:

(x-1/x)^2 =x^2 +(1/x)^2 -2

6^2 = x^2 +(1/x)^2 -2

36 -2 =x^2+ (1/x)^2

34 = x^2 + (1/x)^2

Answer 2

Answer:

Given: x - 1/x = 6

To find: x^2 + 1/x^2 = ?

We know that,

(a-b)^2 = a^2 + b^2 - 2ab

We will use this identity to find the value of x^2 + 1/x^2.

=> (x - 1/x)^2 = x^2 + (1/x)^2 - 2•x•(1/x)

=> (x - 1/x)^2 = x^2 + 1/x^2 - 2

=> (6)^2 = x^2 + 1/x^2 - 2

{ given: x - 1/x = 6 }

=> 36 = x^2 + 1/x^2 - 2

=> x^2 + 1/x^2 = 36 + 2

=> x^2 + 1/x^2 = 38

Thus, the required value of x^2 + 1/x^2 is

38.