Question

The coefficient of x in the expansion of (x+1/ax^2)^7 is 7/3. Find the possible values of a.

Answer 1

are there options?

Answer 2

No,unfortunately not

Answer 3

ok, after expansion the x coefficient is (21/a^2)
\[\frac{7}{3} = \frac{21}{a^{2}}\]
\[a^{2} = \frac{21*3}{7} = 9\]
\[a = \pm 3\]

the term that has x to the power of 1
should be 21/a^2

you need to simplify the terms first

if you simplify that term, you get --> 7/(a^6*x^11)
Use term 21x^5(1/(ax^2))^2 = (21x^5)/(a^2*x^4) = 21x/a^2