Question : If $a + b + c = 0$ and $ab + bc + ca = -11$, then what is the value of $a^2+b^2+c^2$?
Option 1: –11
Option 2: 22
Option 3: 0
Option 4: 11
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Correct Answer: 22
Solution :
Given: $a + b + c = 0$ and $ab + bc + ca = -11$
We know,
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$
$⇒0^2 = a^2 + b^2 + c^2 + 2(-11)$
$\therefore a^2 + b^2 + c^2 = 22$
Hence, the correct answer is 22.
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