Question

If X(3-2/X)=3/X find x2+1/x2=?​

Answer 1

Answer:

22 / 9

Step-by-step explanation:

Given---> x ( 3 - 2 / x ) = 3 / x

To find ---> x² + 1 / x² = ?

Solution---> ATQ

x ( 3 - 2 / x ) = 3 / x

3 x - x ( 2 / x ) = 3 / x

3 x - 2 = 3 / x

3 x - 3 / x = 2

3 ( x - 1 / x ) = 2

Squaring both sides we get

(3)² ( x - 1 / x )² = (2)²

We have an identity

(a - b )² = a² + b² - 2 ab

Applying it we get

9 { (x)² + (1/x)² - 2 x (1 / x ) } = 4

9 ( x² + 1 / x² - 2 ) = 4

x² + 1/ x² - 2 = 4 / 9

x² + 1 / x² = 2 + (4 / 9 )

x² + 1 / x² = 18 + 4 / 9

x² + 1 / x² = 22 / 9