If a^2 + b^2 + c^2 = 20 and a + b + c = 0, find ab + bc + ca.

Question

If a² + b² + c² = 20 and a + b + c = 0, find ab + bc + ca.

A. 10

B. -10

C. 20

D. -20

Answer: B. -10

Solution:

a² + b² + c² = 20 and a + b + c = 0 [ Given ]

We know that, ⇒ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

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

⇒ 0 = 20 + 2(ab + bc + ca)

⇒ −20 = 2(ab + bc + ca)

⇒ ab + bc + ca = −20/2

∴ ab + bc + ca = −10

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