If x3 + y3 + z3 = 3(1 + xyz), P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P3 + Q3 + R3 - 3PQR?
A. 9
B. 8
C. 12
D. 6
Answer: Option C
Solution(By Examveda Team)
x3 + y3 + z3 = 3(1 + xyz)P = y + z - x, Q = z + x - y, R = x + y - z
Put y and z = 0
x3 = 3, P = -x, Q = x, R = x
P3 + Q3 + R3 - 3PQR
= (-x)3 + (x)3 + (x)3 - 3(-x)(x)(x)
= x3 + 3x3
= 4x3
= 4 × 3
= 12
This Question Belongs to Arithmetic Ability >> Algebra
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