Question

If $a^2+b^2+c^2=1,$ then which of the following cannot be the value of $(ab+bc+ca)$?

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{-1}{2}$
• D. $-1$

Answer 1

The correct option is D $-1$

We know that $(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$

$\Rightarrow (a+b+c{)}^2=1+2(ab+bc+ca)$

$(a+b+c{)}^2$ should always be positive

By checking options one by one, we get the result

1)ab+bc+ca=0

$\Rightarrow (a+b+c)^{2}=1$ which can be true

Same way b, c options are true

4th option where ab+bc+ca=-1/2

We get $(a+b+c)^{2}=-1$ which is false