Question

The value of (x-y)(x+y)+(y-z)(y+z)+(z-x)(z+x) is :

a) x+y+z
b) x-y+yz+zx
c) 0​

Answer 1

Answer:

What is the value of xy (X+y) +yz(y+z) +ZX(z+x) +3xyz, when x=a(b-c), y=b(C-a), z=c(a-b)?

If x = a.(b-c). ………….(1).

y = b.(c-a). ……………..(2).

z = c.(a-b). ………………(3).

Adding the eqn.(1) , (2) and (3).

x + y + z = ab -ca+bc -ab +ca -bc.

or, x + y + z = 0. ……………..(4).

xy(x+y)+yz.(y+z)+zx.(z+x) +3xyz.=?

Putting (x+y)=-z , (y+z) = -x and (z+x) = -y from eqn.(4).

= xy(-z) +yz(-x)+zx(-y) +3xyz.

= -3xyz + 3xyz.

= 0. Answer.