Finding range of a equation with given condition. We are given three real number $$a,b,c$$. With the condition $$(a^2+1)(b^2+1)(c^2+1)=9$$
We have to find the number of integers in the range of $$(ab+bc+ca)$$
Ans given is 7.

$(a^2+1)(b^2+1)(c^2+1)=((a+b)^2+(ab-1)^2)(c^2+1)=(ab+bc+ca-1)^2+(a+b+c-abc)^2$
