If $a + b + c = 10$ and $a b + b c + c a = 25$ , find the value of $a^{2} + b^{2} + c^{2} .$

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Solution

The correct option is A 50
Given,
$a + b + c = 10$ and $a b + b c + c a = 25$
We know,
$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$
Thus,
$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$
$=> 10^{2} = a^{2} + b^{2} + c^{2} + 2 (25)$
$=> 100 - 50 = a^{2} + b^{2} + c^{2}$
$=> a^{2} + b^{2} + c^{2} = 50$

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Similar questions

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