<s>[INST] $a^2 + b^2 + c^2 = 1 ,$ then $ab + bc + ca$ gives =? In a recent examination this question has been asked, which says:
$a^2+b^2+c^2 = 1$ , then  $ab + bc + ca$ gives = ?
What should be the answer? I have tried the formula for $(a+b+c)^2$, but gets varying answer like $0$ or $0.25$, on assigning different values to variables.
How to approach such question? 
 [/INST] It depends on $a+b+c$:
$$
(a+b+c)^2-2(ab+bc+ca)=1\\
ab+bc+ca=\dfrac{(a+b+c)^2-1}{2}
$$
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