Question

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

Answer 1

Answer:

How do you find the value of x² + 1/x² given that x = 2+ √3?”

You square X and plug it into the formula given.

Perhaps this is complicated enough to be confusing… so let's do it one step at a time.

We know that we need x²… so let's find that first.

x = 2+ √3, so let's square that.

x² = (2+ √3)(2+ √3)

We remember the FOIL rule, right? First, Outside, Inside, Last. So:

x² = (2+ √3)(2+ √3) = (4 + 2√3 + 2√3 + 3) = 7 + 4√3

So now we know what x² is. Now we want to plug that into x² + 1/x².

The first term is just x², and we know what that is. The second term is one divided by that. So we can add them… and we’re done.