If p + q + r = 13 and pq + qr + rp = 30, then the value of p³ + q³ + r³ − 3pqr is:

Question

Question

This question was previously asked in

RRB Group D 9 Sept 2022 Shift 2 Official Paper

Answer 1

Given :

p + q + r = 13

pq + qr+ rp = 30

Formula used:

x³ + y³+ z³ - 3xyz = (x +y +z) [( x + y + z)² - 3(xy + yz + zx )]

Where, x, y, and z are variables

Calculation:

Here, we have p + q + r = 13 and pq + qr + rp = 30

Now, as we know that

⇒ p³ + q³ + r³ - 3pqr = (p + q + r) [ (p + q + r)² - 3(pq + qr + rp)]

⇒ p³ + q³ + r³ - 3pqr = 13[(13)² - 3 × 30]

⇒ p³ + q³ + r³ - 3pqr = 13[169 - 90]

⇒ p³ + q³ + r³ - 3pqr = 13 × 79 = 1027

Hence, the required value is 1027.

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