Question : If $a+b+c=0$ and $a^2+b^2+c^2=40$, then what is the value of $a b+b c+c a$?
Option 1: –30
Option 2: –20
Option 3: –25
Option 4: –40
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Correct Answer: –20
Solution :
Given: $a+b+c=0$ and $a^2+b^2+c^2=40$
we know that,
$(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)$
Putting the values, we get:
⇒ $0 = 40 + 2(ab+bc+ca)$
⇒ $ab+bc+ca = -\frac{40}{2} = -20$
Hence, the correct answer is –20.
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