If $ a^2 + b^2 + c^2 = 576$ and (ab + bc + ca) = 50, then what is the value of (a + b + c), if ( a + b + c) < 0 ?

-26

Given,

a² + b² + c² = 576

(ab + bc + ca) = 50

We know that,

(a + b + c)² = a² + b² + c²  + 2(ab + bc + ca)

= (a + b + c)² = 576 + 2 × 50 = 676

= (a + b + c) = ±26

But, it is given that (a + b + c) < 0 

So, (a + b + c) = -26