Given x = 2 + √3 and given to find the value of x3 + \(\frac{1}{x^3}\)
We have x = 2 + √3
rationalising factor for denominator is 2 - √3
and also \((x + \frac{1}{x})\) = 2 + √3 + 2 - √3
= 2 + 2 = 4
∴ \((x + \frac{1}{x})\) = 4 equation (i)
We know that,
By putting \((x + \frac{1}{x})\) = 4 we get
∴ The value of x3 + \(\frac{1}{x^3}\) is 52.