Answer:
This is the long way to find the value of x² + 1/x², substitute the given x = 2 + √3 into the variable x.
x² + 1/x²
= (2 + √3)² + 1/(2 + √3)²
= [2² + 2(2)(√3) + (√3)²] + 1/[2² + 2(2)(√3) + (√3)²]
= (4 + 4√3 + 3) + 1/(4 + 4√3 + 3)
= (7 + 4√3) + 1/(7 + 4√3)
= (7 + 4√3)²/(7 + 4√3) + 1/(7 + 4√3)
= ((7 + 4√3)² + 1)/(7 + 4√3)
= (7² + 2(7)(4√3) + (4√3)² + 1)/(7 + 4√3)
= (49 + 56√3 + 48 + 1)/(7 + 4√3)
= (98 + 56√3)/(7 + 4√3)
= 14(7 + 4√3)/(7 + 4√3)
= 14
The short way is by using the calculator
