Question

If x+1/x =2,find x2 + 1/x2

Answer 1

Answer :

x² + 1/x² = 2

Solution :

• Given : x + 1/x = 2
• To find : x² + 1/x² = ?

We have ;

x + 1/x = 2

Now ,

Squaring both the sides , we get ;

=> (x + 1/x)² = 2²

=> x² + (1/x)² + 2•x•(1/x) = 4

=> x² + 1/x² + 2 = 4

=> x² + 1/x² = 4 - 2

=> x² + 1/x² = 2

Hence ,

x² + 1/x² = 2

Moreover :

If x + 1/x = 2 , then

=> (x² + 1)/x = 2

=> x² + 1 = 2x

=> x² - 2x + 1 = 0

=> (x - 1)² = 0

=> x = 1

Thus ,

x² + 1/x² = 1² + 1/1² = 1 + 1 = 2

Also ,

If x + 1/x = 2 , then xⁿ + 1/xⁿ = 2.