Exams › SSC CGL (Prelims) › General

Given that p + q + r = 5, p^3 + q^3 + r^3 = 85, and pqr = 25, determine the value of p^2 + q^2 + r^2 - pq - qr - rp.

1. 2
2. 4
3. 6
4. 8

Correct answer: 2

Solution

Using the identity a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca): LHS = 85 - 3x25 = 85-75 = 10. RHS = 5 x (required expression). So required expression = 10/5 = 2.

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