If a2-b2-c2-16 and a b-b c-c a-10- find the value of a-b-c

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Absolute Value Function

If a2+b2+c2=1...

Question

If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

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Solution

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a + b + c = 10,

a^{2} + b^{2} + c^{2} = 60,

a b + b c + c a

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

a + b + c = 0

\frac{(b + c)^{2}}{b c} + \frac{(c + a)^{2}}{c a} + \frac{(a + b)^{2}}{a b}

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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