If $a + b + c = 9$ and $ab + bc + ca = 23$, find the value of $a^2 + b^2 + c^2$.

Given:

$a + b + c = 9$ and $ab + bc + ca = 23$

To do:

We have to find the value of $a^2 + b^2 + c^2$.

Solution:

We know that,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

Therefore,

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$

$9^2 = a^2 + b^2 + c^2 + 2 \times 23$

$81= a^2 + b^2 + c^2 + 46$

$a^2 + b^2 + c^2 = 81 - 46$

$a^2 + b^2 + c^2 = 35$

Hence, the value of $a^2 + b^2 + c^2$ is $35$.  

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Updated on: 10-Oct-2022

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