Question

If a ² + b ² + c²=
- 83 and a +b+c=15, then find the value of ab+bc+ca​

Answer 1

Answer:

Given,

Given,a+b+c = 15

Given,a+b+c = 15 a²+b²+c² = 83

Given,a+b+c = 15 a²+b²+c² = 83 We know that,

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

a²+b²+c²+2(ab+bc+ca) 15² = 83 + 2(ab+bc+ca)

225 - 83 = 2(ab+bc+ca)

142 = 2(ab+bc+ca)

ab+bc+ca = 142/2

ab+bc+ca = 71

Answer 2

Given:- a²+b²+c²=83 and a+b+c=15

By using identity,

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

(15)² = 83 + 2(ab+bc+ca)

225 - 83 = 2(ab+bc+ca)

142 = 2(ab+bc+ca)

ab+bc+ca = 142/2

ab+bc+ca = 71

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