Question

if a2+b2+c2 = 29 and a+b+c=9 find ab+bc+ac​

Answer 1

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

(9)2=29+2(ab+bc+ca)

81-29=2(ab+bc+ca)

52=2(ab+bc+ca)

52/2=ab+bc+ca

26=ab+bc+ca

Done

Answer 2

Given : a² + b² + c² = 29

a + b + c = 9

To Find :  ab + bc + ac

Solution:

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

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

=> 9² = 29 + 2(ab +  bc +  ac)

=> 81 = 29 + 2(ab +  bc +  ac)

=> 52 = 2(ab +  bc +  ac)

=> 26 = (ab +  bc +  ac)

Hence ab+bc+ac​ = 26

How :

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

LHS  = (( a + b) + c)²

using (x + y)² = x² + y² + 2xy

= (a + b)²  + c²  + 2(a + b) c

= a² + b²  + 2ab + c²   + 2ac + 2bc

= a² + b²  + + c² + 2ab + 2bc + 2ac

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