Question

if x=2+√3, find the value of x² +1/x².
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Answer 1

Step-by-step explanation:

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.

Answer 2

Step-by-step explanation:

x²=(2+√3)²=4+4√3+3=7+4√3

x²+1/x²= (7+4√3)+1/(7+4√3)

= (7+4√3) + (7-4√3)/(7+4√3)(7-4√3)

= (7+4✓3) + (7-4√3)/(49-48)

= 7+4√3 + 7-4√3=14