Question

if x+y+z=0 show that (x+y) ^2/3xy+(y+z)^2/3yz+(3+x) ^2/3zx) =1​

Answer 1

Answer:

Let M = x^2/yz + y^2/zx + z^2/xy

Multiply and divide each term by x, y & z respectively.

=> M = x^3/xyz + y^3/xyz +z^3/xyz

=> M = (x^3 + y^3 +z^3)/xyz

Since x + y + z = 0

x^3 + y^3 + z^3 = 3xyz

=> M = 3xyz/xyz = 3