(x^3+y^3+z^3-3xyz)/(a^3+b^3+c^3-3abc) x (a^2+b^2+c^2 - ab - bc - ca)/(x^2+y^2+z^2 - xy - yz - zx) equals

Question

\(\frac{x^3+y^3+z^3-3xyz}{a^3+b^3+c^3-3abc}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\) equlas

(a) 1 

(b) \(\frac{x^2+y^2+z^2}{a^2+b^2+c^2}\)

(c) \(\frac{x+y+z}{a+b+c}\)

(d) \(\frac{xyz}{abc}\)

Answer 1

(c) \(\frac{x+y+z}{a+b+c}\)

Reqd. exp.

= \(\frac{(x+y+z)(x^2+y^2+z^2-xy-yz-zx)}{(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\)

= \(\frac{x+y+z}{a+b+c}\)