Question

If a+b+c = 0 and a2+b2+c2=16 , find the value of ab+bc+ca

Answer 1

Answer:

The answer is ab+bc+ca= -8

Step-by-step explanation:

Given

a+b+c=0

a²+b²+c²=16

we know that

(a+b+c)²=a²+b²+c2+2(ab+bc+ca)

Therefore

(0)²=16+2(ab+bc+ca)

-16=2(ab+bc+ca)

ab+bc+ca=-16/2=-8

Therefore

ab+bc+ca =-8.

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Answer 2

The value of ab + bc + ca = - 8

Given :

a + b + c = 0 and a² + b² + c² = 16

To find :

The value of ab + bc + ca

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that , a + b + c = 0 and a² + b² + c² = 16

Step 2 of 2 :

Find the value of ab + bc + ca

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

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

⇒ 0² = 16 + 2(ab + bc + ca)

⇒ 16 + 2(ab + bc + ca) = 0

⇒ 2(ab + bc + ca) = - 16

⇒ ab + bc + ca = - 16/2

⇒ ab + bc + ca = - 8

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