Po = a+b = 8
P1 = ax+by = 9
P2 = ax^2 + by^2 = 57
P3 = ax^3 + by^3 = 111
P4 = ax^4 + by^4 = ?
A = x + y, B = x*y
P2 = A*P1 - B*Po
= 9A - 8B
= 57
P3 = A*P2 - B*P1
= 57A - 9B
= 111
=> A = 1, B = -6
=> P4 = A*P3 - B*P2
= 1*111 + 6*57
= 111 + 342
= 453
= answer
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