Using the binomial expansion
(x^2-b/x)^4
= (x^2)^4 + 4(x^2)^3 (-b/x) + 6(x^2)^2 (-b/x)^2 + 4(x^2) (-b/x)^3 + (-b/x)^4
= 4x^8 - 4x^6 (b/x) + 6x^4 b^2/x^2 - ...
= 4x^8 - 4x^5 b + 6x^2 b^2 - ...
so the term containing x^2 is 6x^2 b^2 , which is equal to 294
6v^2 = 294
b^2 = 49
b = ± 7
check by Wolfram:
http://www.wolframalpha.com/input/?i=expand+(x%5E2-7%2Fx)%5E4
http://www.wolframalpha.com/input/?i=expand+(x%5E2%2B7%2Fx)%5E4
In the expansion of (x^2-b/x)^4, the coefficient of x^2 is 294. Find the value of the constant "b"
1 answer