If (a+x)^n is expanded in increasing order of x.find the value of n if the coefficients x^2 and x^n-2
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Answer:
4×.n2-4×+1n
4×.n2-4×:n
ans is n-4
just like this
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Given : (a + x)ⁿ expanded in increasing order of x
To find : value of n if the coefficients x² and xⁿ⁻² are same
Solution:
(a + x)ⁿ
= aⁿ + ⁿC₁aⁿ⁻¹x + ⁿC₂aⁿ⁻²x² + .............................+ ⁿCₙ₋₂a²xⁿ⁻² + ⁿCₙ₋₁a¹xⁿ⁻¹ + xⁿ
Coefficient of x² & xⁿ⁻² are equal
=> ⁿC₂aⁿ⁻² = ⁿCₙ₋₂a²
ⁿC₂ = ⁿCₙ₋₂
=> aⁿ⁻² = a²
Equating powers
=> n -2 = 2
=> n = 4
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