Question

If x=3+2√2, find the value of x²+1/x²​

Answer 1

Answer:

x = 3+2√2

and,

1/x = 1/3+2√2 = 3-2√2/(3+2√2)(3-2√2) = 3-2√2/9-8 = 3-2√2

Now,

x = 3+2√2

and,

1/x = 3-2√2

Squaring x

x^2 = 9+8+12√2

= 17+12√2

And,

1/x^2 = 9+8-12√2 = 17-12√2

So,

x^2 + 1/x^2 = (17+12√2)+(17-12√2) = 34

Hope this helps you !