Question

the second, third and fourth term of the binomial expansion (x+a)n (n is actually (x+a)raised to the power n) are 240, 720 and 1080. find x, a and n.

Answer 1

Here is your answer:
See the attached pictures. After the picture is given below:
Putting value of n from equation 7 in equations 5 and 4,

equation 5 is 4a = 6x or 2a = 3x -----(8)
and,
equation 4 is 5a x⁴ = 240 or x⁴ = 48/a ------(9)

put value of a from equation 8 in equation 9,
we get,
x⁴ = 48•2/3x
x⁵ = 16•2
x⁵ = 2⁵
which implies,
x = 2, and so,
a = 3.


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