The coefficient of x^2 in the expansion of (k+(1/3)x)^5 is 30. Find the value of the constant k.
jeew-m | Certified Educator
Using binomial theorem;
`(k+(1/3)x) = sum_(r=0)^5^5C_r (x/3)^r k^(5-r)`
The coefficient of `x^2` can be obtained when r = 2.
Coefficient of `x^2 = ^5C_2 (1/3)^2 k^5-2 = 30`
`(10/9) xx k^3 = 30`
`K^3 = 27`
So the value of k is 3.