If a + b = m, a²+ b² = n and a³ + b³ = p³ then what is the value of m³ + 2p³?

প্রশ্ন: If a + b = m, a²+ b² = n and a³ + b³ = p³ then what is the value of m³ + 2p³?

সমাধান:
দেওয়া আছে,
a + b = m
a² + b² = n

এখন,
m³ + 2p³
= (a + b)³ + 2(a³ + b³)
= a³ + 3a²b + 3ab² + b³ + 2a³ + 2b³
= 3a³ + 3a²b + 3ab² + 3b³
= 3(a³ + a²b + ab² + b³)
= 3{a²(a + b) + b²(a + b)}
= 3(a + b)(a²+b²)
= 3 ⋅ m ⋅ n
= 3mn