### Question

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

^{2}+ b

^{2}+ c

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

A. 10

B. -10

C. 20

D. -20

**Answer: B. -10**

**Solution**:

a^{2} + b^{2} + c^{2} = 20 and a + b + c = 0 [ Given ]

We know that, ⇒ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca

⇒ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)

⇒ 0 = 20 + 2(ab + bc + ca)

⇒ −20 = 2(ab + bc + ca)

⇒ ab + bc + ca = −20/2

**∴ ab + bc + ca = −10**

**Read More:**

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