Question
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?Solution
P = y + z – x, Q = z + x – y and R = x + y – 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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