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  • 12. If p is a real number and the middle term in the expansion(p/2 + 2)^8 is 1120, then find the value of p.

If p is a real number and the middle term in the expansion (p/2 + 2)8 is 1120, then find the value of p.

Answers (1)

Given: (p/2 + 2)8

Now, here index is n = 8,

Since there is only one middle term, viz., (8/2 + 1)th i.e., the fifth term

T5 = T4+1

     = 8C4(p/2)8-4. 24

Now,

1120 = 8C4p4

1120 = 8x7x6x5x4!/4!x4x3x2x1 . p4

1120 = 7x2x5xp4

Thus, p4 = 1120/70

                 p4= 16

                 p2 = 4

Thus,       p = ±2

Posted by

infoexpert22

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