Question

a^n/(a-b)(a-c)+b^n/(b-c)(b-a)+c^n/(c-a)(c-b)

Answer 1

Step-by-step explanation:

(i) ab - bc, bc - ca, ca - ab

(ii) a - b + ab, b - c + bc, c - a + ac

(iii) 2p^2q^2-3pq+4,\ 5+7pq-3p^2q^22p

2

q

2

−3pq+4, 5+7pq−3p

2

q

2

(iv) l^2+m^2,\ m^2+n^2,n^2+l^2+2lm+2mn+2nl

2

+m

2

, m

2

+n

2

,n

2

+l

2

+2lm+2mn+2n

Solution:

(i) ab - bc, bc - ca, ca - ab

(ii) a - b + ab, b - c + bc, c - a + ac

Hence the sum if 0.

Hence the sum is ab + bc + ac

(iii) 2p^2q^2-3pq+4,5+7pq-3p^2q^22p

2

q

2

−3pq+4,5+7pq−3p

2

q

2

(iv) l^2+m^2,m^2+n^2,n^2+l^2,2lm+2mn+2nll

2

+m

2

,m

2

+n

2

,n

2

+l

2

,2lm+2mn+2nl

Hence the sum is -p^2q^2+4pq+9−p

2

q

2

+4pq+9

Hence the sum is

2\left(l^2+m^2+n^2+lm+mn+nl\right)2(l

2

+m

2

+n

2

+lm+mn+nl)