If ⁻¹ x+ ⁻¹ y+ ⁻¹ z=3 , then x(y+z)+y(z+x)+z(x+y) equals to

Step-by-step solution

Given, ⁻¹(x)+ ⁻¹(y)+ ⁻¹(z)=3 As, we know that 0 ⁻¹(x) Thus, the maximum value of ⁻¹(x)= satisfies the given equation. x=y=z= =-1 Now, x(y+z)+y(z+x)+z(x+y)=x y+z x+y z+x y+z x+y z=2(x y+y z+z x)=2(1+1+1)=6