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