#binomial expansion

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wraith bramble Nov 10, 2022, 9:13 PM

Is there a way to find n and k without using trial and error with factors of 24

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sleek swallow Nov 10, 2022, 9:16 PM

so we know nC1 * 1^(n-1) * kx = 24x
and nC2 * 1^(n-2) * (kx)^2 = 240x^2

so nk = 24 and
n!/(n-2)!2! * k^2 = 240

n! = n(n-1)(n-2)!

so n(n-1)/2 * k^2 = 240

solve simultaneously