If a + b + c = 9 and ab + bc + ca = 23,
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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