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Question
If p is a real number and if the middle term in the expansion of `(p/2 + 2)^8` is 1120, find p.
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Solution
Given expression is `(p/2 + 2)^8`
Number of terms = 8 + 1 = 9 (odd)
∴ Middle term = `(9 + 1)/2` th term = 5th term
∴ T5 = T4+1
= `""^8"C"_4 (p/2)^(8 - 4) (2)^4`
= `""^8"C"_4 p^4/2^4 xx 2^4`
= `""^8"C"_4 p^4`
Now 8C4P4 = 1120
⇒ `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1) "P"^4` = 1120
⇒ 70P4 = 1120
⇒ P4 = `1120/70` = 16
⇒ P4 = 24
⇒ P = ±2
Hence, the required value of P = ±2
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