InterviewSolution
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InterviewSolution
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If the sum of the coefficients in the expansion of `(b + c)^(20) {1 +(a -2) x}^(20)` is equal to square of the sum of the coefficients in the expansion of `[2 bcx - (b + c)y]^(10)`, where a, b, c are positive constants, thenA. ` ge sqrt((a c)`B. `(b +c)/(2) ge a`C. c, a and b are in G. PD. `(1)/(c),(1)/(a),(1)/(b)` are in H.P |
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Answer» Correct Answer - b The sum of the coefficients in the expansion of `(b + c )^(20){1 + (a - 2)x}^(20)` is given by `S_(1) = ( b + c)^(20) (a - 1)^(20)` [ Putting x = 1] The sum of the coefficients in the expansion of `[2 bcx - (b + c)y]^(10)` is given by `S_(2) = [ 2 bc - (b + c)]^(10)` [ Putting x = y = 1]` If is given that `S_(1) = S_(2)""^(2)` `rArr (b + c)^(20) (a -1)^(20) = (2bc - b - c )^(20)` `rArr (b + c ) (a -1) - =2bc - b - c` `rArr a - 1 = (2bc)/(b +c) - 1` `rArr a= (2 bc)/(b+c)` `rArr a ` is the H.M of of b and c. But, `(b +c)/(2)` is the A. M. of b and c. Therefore, A. M. `ge` H.M.`rArr (b+c)/(2) ge a` . |
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