Math miscellaneousEasy
Question
For natural numbers m, n if (1 - y)m (1 + y)n = 1 + a1y + a2y2 + ...., and a1 = a2 = 10, then (m, n) is
Options
A.(20, 45)
B.(35, 20)
C.(45, 35)
D.(35, 45)
Solution
(1 - y)m(1 + y)n = [1-mC1y+mC2y2 - ...][1 + nC1y + nC2y2 + ....]
= 1 + (n - m) +
y2 + .....
∴ a1 = n - m = 10 and a2 =
= 10
So, n - m = 10 and (m - n)2 - (m + n) = 20 ⇒ m + n = 80
∴ m = 35, n = 45
= 1 + (n - m) +
y2 + .....∴ a1 = n - m = 10 and a2 =
= 10So, n - m = 10 and (m - n)2 - (m + n) = 20 ⇒ m + n = 80
∴ m = 35, n = 45
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