Question

if a2+b2+c2=20 and a+ b+c=0 find ab+ bc+ ca

Answer 1

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

Solution :

Given :-
a² + b² + c² = 20
a+b+c = 0

Using this formula :
(a+b+c)² = a² + b² + c² + 2(ab + bc + ca)

So,

(0)² = 20 + 2(ab + bc + ca)

=> 0 = 20 + 2(ab + bc + ca)

=> -20 = 2(ab + bc + ca)

=> -20/2 = (ab + bc + ca)

=> -10 = (ab + bc + ca)

Hence,
ab+ bc+ca = -10

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Verification :-

a² + b² + c² + 2(ab + bc + ca)

= 20 + 2(-10)

= 20 - 20

= 0

Answer 2

Answer:

-10

Step-by-step explanation:

a+b+c=0

Square on both side

(a+b+c)2=02

a2+b2+c2+2ab+2bc+2ca=0

a2+b2+c2+2(ab+bc+ca)=0           (given a2+b2+c2=20)

20+2(ab+bc+ca)=0  

2(ab+bc+ca)=-20

ab+bc+ca=-20/2

=-10