P + 3/P = 5 হলে, P⁶ - 80P³ = কত?

প্রশ্ন: P + 3/P = 5 হলে, P⁶ - 80P³ = কত?

সমাধান:
দেওয়া আছে,
P + 3/P = 5
⇒ (P + 3/P)³ = 5³
⇒ P³ + (3/P)³ + 3 × P × 3/P × (P + 3/P) = 125
⇒ P³ + (27/P³) + 9 × 5 = 125
⇒ P³ + (27/P³) + 45 = 125
⇒ P³ + (27/P³) = 125 - 45
⇒ P³ + (27/P³) = 80
⇒ P⁶ + 27 = 80P³
∴ P⁶ - 80P³ = - 27