Question

If [x+(1/x)]=3 then what is [x^2+(1/x^2)]=?

Answer 1

Note:

(a+b)^2 = a^2 + b^2 + 2•a•b

Given:

x + 1/x = 3

To find:

x^2 + 1/x^2 = ?

we know that;

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

=> (3)^2 = x^2 + 1/x^2 + 2

=> 9 = x^2 + 1/x^2 + 2

=> x^2 + 1/x^2 = 9 - 2

=> x^2 + 1/x^2 = 7

Hence,

The required value of x^2 + 1/x^2 is 7.