Question

If the mean of y and 1/y is z, then mean
of y^2 and 1/y^2 is,
​

Answer 1

Answer :

2z² - 1

Solution :

• Given : ½(y + 1/y) = z
• To find : ½(y² + 1/y²) = ?

We have ,

→ ½(y + 1/y) = z

→ y + 1/y = 2z

Now ,

Squaring both the sides , we get ;

=> (y + 1/y)² = (2z)²

=> y² + (1/y)² + 2•y•(1/y) = 2²z²

=> y² + 1/y² + 2 = 4z²

=> y² + 1/y² = 4z² - 2

=> y² + 1/y² = 2(2z² - 1)

=> ½(y² + 1/y²) = 2z² - 1

Hence ,

Mean of y² and 1/y² is (2z² - 1) .