Question

if x+y+z=0 then prove xyz/(x+y)(y+z)(z+x)=-1 where x!=-y y!=-zz!=-x

Answer 1

I don't know why that whole factorial thing is given there do you think the answer could be this way I am not sure

Answer 2

Answer:

It is given that x+y+z = 0 ............(1)

where x≠ -y, y≠ -z , z≠ -x

We nee to prove:

$\frac{xyz}{(x+y)(y+z)(z+x)}$ = -1 ...........(2)

From (1), we get x+y = -z

y+z = -x

x+z = -y

Putting the values of (x+y), (y+z), (z+x) in the denominator of equation (2), we get

$\frac{xyz}{-z \times -x \times -y}$ = $\frac{xyz}{-xyz}$

                                                                  = -1

Therefore, L.H.S = R.H.S

Hence, proved