Let α 0, β 0 be such that α³ + β² = 4. If the maximum value of the term independent of x in the binomial expansion of (αx^(1/9) + βx^(-1/6))¹⁰ is 10k, then k is equal to:

Question

Let α > 0, β > 0 be such that α³ + β² = 4. If the maximum value of the term independent of x in the binomial expansion of (αx^(1/9) + βx^(-1/6))¹⁰ is 10k, then k is equal to:

Accepted Answer

336. Exponent zero gives r=4, term = C(10,4) a^6 b^4 = 210 a^6 b^4. With u=a^3, v=b^2 and u+v=4, a^6 b^4 = u^2 v^2 is max at u=v=2 giving 16. Max term = 210*16 = 3360 = 10k, so k = 336.

Let α > 0, β > 0 be such that α³ + β² = 4. If the maximum value of the term independent of x in the binomial expansion of (αx^(1/9) + βx^(-1/6))¹⁰ is 10k, then k is equal to:

Solution

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