Question
If x3Β + y3Β + z3Β =
3(1 + xyz), P = y + z β x, Q = z + x β y and R = x + y β z, then what is the value of P3Β + Q3Β + R3β 3PQR?Solution
P = y + z β x, Q = z + x β y and R = x + y β z And x3 + y3 + z3 = 3(1 + xyz); Suppose x = y = 0 then z3 = 3; P = z, Q = z and R = -z; Putting these values in below equation P3 + Q3 + R3 - 3PQR = z3 + z3 - z3 + 3z3 => 4z3 Putting z3 = 3: P3 + Q3 + R3 - 3PQR = 12
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