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If in the expansion of (2x+5)^(10) , the...

If in the expansion of `(2x+5)^(10)` , the numerically greatest term in equal to the middle term, then find the values of `x`

Text Solution

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The correct Answer is:
`x in (-3,-25/12) uu (25/12,3)`
In the expansion of `(2x+5)^(10)`, the middle term is `T_(6)` .
Consider the expansion of `(1+2x//5)^(10)` .Now
`|(T_(6))/(T_(5))|gt1` and `|(T_(7))/(T_(6))|lt 1`
`rArr |(10-5+1)/(5)(2x)/(5)|gt1` nd `|(10-6+1)/(6)(2x)/(5)|lt1`
`rArr |(12)/(25)x|gt1` and `|(x)/(3)|lt1`
`rArr (25)/(12)lt|x|lt3`
`rArrx in (-3,-25/12)uu(25/1,3)`
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