Question

If x+y+z=0 and x^2+y^2+z^2= 12 then find the value of xy+yx+zx?

Answer 1

Answer:

Step-by-step explanation:

Use AM-GM inequality.

x^2 + y^2 >(or equal) 2xy

y^2 + z^2 > 2yz

z^2 + x^2 > 2xz

Adding all the equations.

x^2+y^2+z^2-xy-yz-xz >(or equal) 0

Since its given that the equation is equal to zero, we conclude that equation has its minimum value.  

So, all the 3 equations should individually attain their minimum values  

So,

x^2+y^2-2xy=0

(x-y)^2=0

So, x=y

Similarly, y=z and x=z.

So, x=y=z

Answer 2

Answer:

Step-by-step explanation: