Question : If $a+b+c=13$ and $a b+b c+c a=45$, find $a^2+b^2+c^2$.
Option 1: 79
Option 2: 65
Option 3: 57
Option 4: 85
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Correct Answer: 79
Solution :
Given: $a+b+c=13$ and $ab+bc+ca=45$
$a^2 + b^2 + c^2 = (a + b + c)^2 - 2 (ab + bc + ca)$
$= 13^2-2\times 45$
$= 169-90 = 79$
Hence, the correct answer is 79.
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