Question

x+1/x=7 then x^2+1/x^2.​

Answer 1

Answer:

x²+1/x² = 51

Step-by-step explanation:

Given x - 1/x = 7 ---(1)

______________________

We know the algebraic identity:

a²+b²-2ab = (a-b)²

Or

a²+b² = (a-b)²+2ab

______________________

Now,

x²+1/x²

= (x-1/x)²+2*x*(1/x)

= (x-1/x)²+2

= 7²+2 [ from (1)]

= 49+2

= 51

Therefore,

x²+1/x² = 51