It is known that $ (ax + b)^6$ has coefficient of $x^2 = 520$, and coefficient of \(x^5 = 3

Question

It is known that $ (ax + b)^6$ has coefficient of $x^2 = 520$, and coefficient of $x^5 = 384$. Find $a$ and $b$. Hence determine the coefficient of $x^3$.

Accepted Answer

$a=\pm2\left(\dfrac{24}{13}\right)^{\frac1{18}},\ b=\pm2\left(\dfrac{13}{24}\right)^{\frac5{18}}$, with matching signs. Coefficient of $x^3=1280\left(\dfrac{13}{24}\right)^{\frac23}$.

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

Solution:

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