Question
If p3 + 9p2 + 8p + 13 =
6p2 + 5p + 12, then find the value of {(p4 + 1/p2)}/(p2 + 3p + 1).Solution
ATQ, Given, p3 + 9p2 + 8p + 13 = 6p2 + 5p + 12 Or, p3 + 9p2 – 6p2 + 8p – 5p + 13 – 12 = 0 Or, p3 + 3p2 + 3p + 1 = 0 Since, (x + y)3 = x3 + 3x2y + 3xy2 + 1 Therefore, (p + 1)3 = 0 Or, p = -1 Therefore, {(p4 + 1/p2 )}/(p2 + 3p + 1) Putting p = -1, we get {(p4 + 1/p2 )}/(p2 + 3p + 1) = (1 + 1)/(1 – 3 + 1) = -2
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