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The coefficient of x^2 in the expansion of (k+(1/3)x)^5 is 30. Find the value of the...

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The coefficient of x^2 in the expansion of (k+(1/3)x)^5 is 30. Find the value of the constant k.

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`(k+1/3x)^5`

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`

`k= 3`

So the value of k is 3.

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