p3 + q3 + r3 – 3pqr = 4, If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3+ c3 – 3abc?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 8
p3 + q3 + r3 – 3pqr = 4 .....(1)
Let, a = q + r
b = r + p
c = p + q
a3 + b3+ c3 – 3abc = 1/2(a + b + c)[(a - b)2 + (b - c)2 + (c - a)2]
= 1/2[2(p + q + r)][(q - p)2 + (r - q)2 + (p - r)2]
= 2[p3 + q3 + r3 – 3pqr]
= 2 × 4 = 8