Question

if a+b+c=15 and a²+b²+c²=65 then find the value of ab+bc+ca​

Answer 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!!

Answer 2

Answer:

a+b+c=15

A2 +b2+c2=65

ab+bc+ca=80