If a² + b² + c² = 576 and (ab + bc + ca) = 50 , then what is the value of (a + b + c), if (a+b+c) < 0 ?
$[2 M a r k s]$

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Solution

(a + b + c)² = a² + b² +c² + 2 (ab + bc + ca)
(a + b + c)² =576 + 2 x 50
$[1 M a r k]$
(a + b + c)² = 676
a + b + c = 26 or -26
a + b + c < 0
so a+b+c = -26
$[1 M a r k]$

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If a + b + c = 0, then write the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b} .$

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