−7 , where a is a constant. Find the value of aIt is given that the constant term in the expansion of (2+x1)2(1−3x)n2 is 67 , where n is a positive integer. Find the value of n.(4+x4+x21)[C0n+Cdn(−3x)+C2n9
Q. −7 , where a is a constant. Find the value of aIt is given that the constant term in the expansion of (2+x1)2(1−3x)n2 is 67 , where n is a positive integer. Find the value of n.(4+x4+x21)[C0n+Cdn(−3x)+C2n9
Simplify Expression: Identify the general form of the expression and simplify the first part.(2+x1)2=4+x4+x21
Expand Using Binomial Theorem: Expand the second part using the binomial theorem.(1−3x)n2=C0n(−3x)0+C1n(−3x)1+C2n(−3x)2+…
Combine and Find Constant Term: Combine the expansions and look for the constant term.(4+x4+x21)(C0n+C1n(−3x)+C2n(9x2)+…)To find the constant term, match powers of x to zero:- From 4⋅C1n(−3x), x-term coefficient is −12C1n- From x21⋅9C2nx2, constant term is 9C2n
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