Question
If x4 + x3 + x2 + x + 1
= 0, then find the value of x1525 + x720 + 14 + x320 =?Solution
From question: x4 + x3 + x2 + x + 1 = 0 ---------(eq 1) Multiply x4 + x3 + x2 + x + 1 = 0 by x x5 + x4 + x3 + x2 + x = 0--------- (eq 2) eq (2) – (1), we will get, => x5 + x4 + x3 + x2 + x - x4 - x3 - x2 - x – 1 = 0 => x5 – 1 = 0 => x5 = 1 => x1525 + x720 + 14 + x320 => (x5)305 + (x5)144 + 14 + (x5)64 => 1 + 1 + 14 + 1 => 17
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