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Let (2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )x^(r ), then the value of (a_(7))/(a_(13)) is |
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Answer» `6` Replacing `x` by `(2)/(x)`, we get `((8)/(x^(2))+(6)/(x)+4)^(10)=sum_(r=0)^(20)a_(r )((2)/(x))^(r )` `implies2^(10)(2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )2^(r )x^(20-r)` `impliessum_(r=0)^(20)a_(r )x^(r )=sum_(r=0)^(20)a_(r )2^(r-10)x^(20-r)` Comparing coefficient `x^(7)` both SIDES , we get `a_(7)=a_(13)xx2^(3)`. |
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