Question : If $a+b+c=15$ and $a b+b c+c a=22$, then find the value of $a^2+b^2+c^2$.
Option 1: 131
Option 2: 141
Option 3: 161
Option 4: 181
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Correct Answer: 181
Solution :
Given:
$a+b+c=15$ and $a b+b c+c a=22$
$(a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca)$
⇒ $(15)^2 = a^2+b^2+c^2+2(22)$
⇒ $225 = a^2+b^2+c^2+44$
⇒ $a^2+b^2+c^2 = 181$
Hence, the correct answer is 181.
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