Question

p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3​

Answer 1

Answer:

Step-by-step explanation:

Given Equation is p³(q - r)³ + q³(r - p)³ + r³(p - q)³

⇒ [p(q - r)]³ + [q(r - p)]³ + [r(p - q)]³

Let a = p(q - r), b = q(r - p), c = r(p - q)

∴ a + b + c = p(q - r) + q(r - p) + r(p - q)

                = pq - pr + qr - qp + rp - rq

                = 0

We know that when a + b + c = 0, then a³ + b³ + c³ = 3abc

⇒ 3(pq - qr)(qr - qp)(rp - rq)

⇒ 3pqr(p - q)(q - r)(r - p)