if a+b+c=15 and a²+b²+c²=65 then find the value of ab+bc+ca
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Answered by
1
Given,
a + b + c = 15
a² + b² + c² = 65
FIND: ab + bc + ca
- Identity to use: (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
- substituting the values,
- (15)² = 65 + 2ab + 2bc + 2ca
- 225 = 65 + 2(ab + bc + ca) [as 2 is common]
- 225 - 65 = 2(ab + bc + ca)
- 160 = 2(ab + bc + ca)
- 160/2 = ab + bd + ca
- 80 = ab + bc + ca
Hope it helps!!
Have a great day!!
Answered by
1
Answer:
a+b+c=15
A2 +b2+c2=65
ab+bc+ca=80
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