Question:
If $a+b+c=9$ and $a b+b c+c a=23$, find value of $a^{2}+b^{2}+c^{2}$
Solution:
We know that,
$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(a b+b c+c a)$
$9^{2}=a^{2}+b^{2}+c^{2}+2(23)$
$81=a^{2}+b^{2}+c^{2}+46$
$a^{2}+b^{2}+c^{2}=81-46$
$a^{2}+b^{2}+c^{2}=35$
Hence, value of required expression $a^{2}+b^{2}+c^{2}=35$
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