Question

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

Answer 1

Step-by-step explanation:

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

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