The expansion of (x-y)^n, n 5 is done in the descending powers of x . If the sum of the fifth and sixth terms is zero, then x y is equal to

Step-by-step solution

(x-y)^ n , n 5 General term, T _ r +1 = n _ c _ r x ^ n - r (- y )^ r . aligned & T ₅+ T ₆=0 & [ n _ c ₄ x ^ n -4 (- y )^4 ]+ [ n _ c ₅ x ^ n -5 (- y )^5 ]=0 & n _ c ₄ x ^ n -4 y ^4- n _ c ₅ x ^ n -5 y ^5=0 & n _ c ₄ x ^ n -4 y ^4= n _ c ₅ x ^ n -5 y & x ^ n -4- n +5 y = n _ c ₅ n _ c ₄ x y = n ! 5!( n -5)! 4!( n -4)! n ! & = 4!( n -4)( n -5)! 5 4!( n -5)! = n -4 5 aligned