If p + q + r = pqr = 1/p + 1/q +1/r = 1 then find p³ + q³ + r³.

If p + q + r = pqr = 1/p + 1/q +1/r = 1 then find p³ + q³…

If p + q + r = pqr = $\frac{1}{p} + \frac{1}{q} +\frac{1}{r}$ = 1 then find p³ + q³ + r³.

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1.

1/p + 1/q + 1/r = 1

⇒ (qr + pr + pq)/pqr = 1

⇒ qr + pr + pq = 1

Now, (p + q + r)² = p² + q² + r² + 2(pq + qr + rp)

⇒ 1² = p² + q² + r² + 2(1)

⇒ 1 = p² + q² + r² + 2

⇒ p² + q² + r² = -1

Also, p³ + q³ + r³ - 3pqr = (p + q + r)(p² + q² + r² - pq - qr - rp)

⇒ p³ + q³ + r³ - 3(1) = (1)(-1 - 1) = -2

⇒ p³ + q³ + r³ = -2 + 3 = 1

Therefore, the value of the expression is 1.