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12. Given that the coefficient of x² in the expansion of (1-ax)' is 60 and that a > 0, find the value of a.​

User Raouaoul
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The binomial expansion of (1-ax)' is:
(1-ax)' = 1 - ax + a²x² - a³x³ + ...

To find the coefficient of x², we need to look at the term with x², which is a²x². Therefore, the coefficient of x² in the expansion is a².

Given that the coefficient of x² is 60, we can solve for a:

a² = 60
a = ±√60

Since a > 0, we take the positive square root:

a = √60 = √(2²×3×5) = 2√15

Therefore, the value of a is 2√15.
User Josh Ribeiro
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