If x + \(\frac{1}{x}\) = 3, then find x⁷ + \(\frac{1}{x^7}\).

843

Imp Note → [Unit digit of x + \(\frac{1}{x}\) will always same as unit digit of x⁷ + \(\frac{1}{x^7}\)]

Formula → [x⁷ + \(\frac{1}{x^7}\) = (x³ + \(\frac{1}{x^3}\)) (x⁴ + \(\frac{1}{x^4}\)) - (x + \(\frac{1}{x}\))]

Remember → If x + \(\frac{1}{x}\) = 3, then x³ + \(\frac{1}{x^3}\) = 18 and x⁴ + \(\frac{1}{x^4}\) = 47

Now; apply formula ⇒

18 × 47 - 3 = 843

Tricks: use unit digits only