If $a^{2} + b^{2} + c^{2} = 60$ and $a b + b c + c a = 42$ . Find the value of $a + b + c$

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Solution

The correct option is C 12
Given,
$a^{2} + b^{2} + c^{2} = 60$ and $a b + b c + c a = 42$
We know,
$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$
Thus,
$(a + b + c)^{2} = (a^{2} + b^{2} + c^{2}) + 2 (a b + b c + c a)$
$=> (a + b + c)^{2} = 60 + 2 (42)$
$=> (a + b + c)^{2} = 60 + 84$
$=> (a + b + c) = \sqrt{144}$
$=> (a + b + c) = 12$

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Similar questions

a + b + c = 12

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a^{2} + b^{2} + c^{2}

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If $a + b + c = 0$ then find value of $\frac{a^{2}}{b c} + \frac{b^{2}}{a c} + \frac{c^{2}}{a b}$

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