Question

c) Factorise
(i) (a - b) c + (b2 - c) a
(ii) a2(y- z) - b(z - y) + c2(y – z)

Answer 1

Answer:

1) If x,y,z are in A.P. , xy=z−y

a2(b+c)−a2(b+c)=c2(a+b)−b2(c+a)

a2b+a2c−a2b−a2c=c2a+c2b−b2c−b2a

(a2b−a2c)+(b2a−a2b)=(c2a−b2a)+(c2b−b2c)

c(b2−a2)+ab(b−a)=a(c2−b2)+bc(c−b)

(b−a)[c(b+a)+ab]=(c−b)[a(c+b)+bc]

(b−a)(bc+ac= 0

b- a =c - b

a,b,c are in A.P.

2)

a=b

2xa=(c2y)

2xora=c4

xyora=(a2z)

4xyora=a8xyz

∴8xyz=1∴xyz=(81)