Question

A=x(y-z),b=y(z-x),c=z(x-y) find the value of (a/x)3+(b/y)3+(c/z)3

Answer 1

Answer:

3(-x^2y-xz^2+x^2z-y^2z+xy^2+yz^2)

Step by step explanation:

a=xy-xz,b=yz-xy,c=zx-yz

then,

a/x=(xy-xz)/x

b/y=(yz-xy)/y

c/z=(zx-yz)/z

so,taking x,y and z as common in a/x,b/y and c/z

x(y-z)/x=y-z=a

y(z-y)/y=z-x=b

z(x-y)/z=x-y=c

as we know when a+b+c=0, a^3+b^3+c^3=3abc

a+b+c=y-z+z-x+x-y

=0

therefore a^3+b^3+c^3=3(y-z)(z-x)(x-y)

=xyz-x^2y-xz^2+x^2z-y^2z+xy^2+yz^2-xyz

=3(-x^2y-xz^2+x^2z-y^2z+xy^2+yz^2)