Find the value of a for which there is no term independent of x in the ezlxpansion of
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"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.

Recall the binomial theorem:

So we have

The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:

which reduces to

2160a - 4320 = 0

2160a = 4320

a = 2

ratio is 2 : 9

the answer is three

13.5 : 3