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If the `4^(th)` term in the expansion of `( 2 + 3x/8)^10` has the maximum value, then the values of x for which this will be true is : |
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Answer» `T_4` in `(2+(3x)/8)^10 = C(10,3)(2^7)((3x)/8)^3` `T_3` in `(2+(3x)/8)^10 = C(10,2)(2^8)((3x)/8)^2` `T_5` in `(2+(3x)/8)^10 = C(10,4)(2^6)((3x)/8)^4` Now, we are given `T_4` has the maximum value. So,`T_4 gt t_3` `=> C(10,3)(2^7)((3x)/8)^3 gt C(10,2)(2^8)((3x)/8)^2` `=>C(10,3)((3x)/8) gt C(10,2)(2)` `=>(10**9**8)/(3**2**1)((3x)/8) gt (10**9)/(2**1)(2)` `45x gt 90=> x gt 2` Also, `T_5 lt T_4` `=> C(10,4)(2^6)((3x)/8)^4 lt C(10,3)(2^7)((3x)/8)^3` `=>C(10,4)((3x)/8) lt C(10,3)(2)` `=>(10**9**8**7)/(4**3**2**1)((3x)/8) lt (10**9**8)/(3**2**1)(2)` `=>630x/8 lt 240` `=>x lt 192/63 => x lt 64/21` So, `2 lt x lt 64/21`, is the value for which `x` will be true. |
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