InterviewSolution
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InterviewSolution
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If p is a real number and the middle term in the expansion of `((p)/(2) + 2)^(8)` is 1120, then find the value of p. |
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Answer» Given expansion is `((p)/(2) + 2)^(8)` Hence, `n = 8` Since, this Binomial expansion has only one middle term i.e., `((8)/(2) + 1)th = 5 th` term `T_(5) = T_(4 + 1) = .^(8)C_(4) ((p)/(2))^(8 - 4) .2^(4)` `rArr 1120 = .^(8)C_(4) p^(4) .2^(-4) 2^(4)` `rArr 1120 = (8 xx 7 xx 6 xx 5 xx 4!)/(4! xx 4 xx 3 xx 2 xx 1)p^(4)` `rArr 1120 = 7 xx 2 xx 5 xx p^(4)` `rArr p^(4) = (1120)/(70) = 16 rArr p^(4) = 2^(4)` `rArr p^(2) = 4 rArr p = -+ 2` |
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