Question

If a 2 +b 2 +c 2 =250 and ab+bc+ca=3 then find abc

Answer 1

(a + b + c)² = (a + b + c)(a + b + c) 

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

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

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

(a + b + c)² = (a² + b² + c²) + 2(ab + bc + ac) → you know that: a² + b² + c² = 250 

(a + b + c)² = 250 + 2(ab + bc + ac) → you know that: ab + bc + ca = 3 

(a + b + c)² = 250 + 6 

(a + b + c)² = 256 

a + b + c = ± 16 ← answer A