Question

If a² + b² + c² = 50 and ab + bc + ca = 47, find a + b + c.

Answer 1

a² + b² + c² = 50 and ab + bc + ca = 47
Since ( a + b + c )² = a² + b² + c² + 2( ab + bc + ca )
∴ ( a + b + c )² = 50 + 2(47)
⇒ ( a + b + c )² = 50 + 94 = 144
⇒ a + b +c = ${\displaystyle \sqrt{144}=\pm 12}$
∴ a + b + c = ${\displaystyle \pm 12}$