Q20.If a^2 + b^2 + c^2 = 155 and a + b + c = 21, find ab + bc + ca.

2 thoughts on “Q20.If a^2 + b^2 + c^2 = 155 and a + b + c = 21, find ab + bc + ca.”

1. Step-by-step explanation:

   2

   +b

   2

   +c

   2

   =250 & ab+bc+ac=3, find a+b+c

   → the general formula

   (a+b+c)

   2

   =a

   2

   +b

   2

   +c

   2

   +2(ab+bc+ac)

   =250+2(3)

   =250+6

   ∴(a+b+c)

   2

   =256

   ∴a+b+c=

   256

   ∴a+b+c=16

   Hope it helped!!

   Reply

2. Answer:

   since,

   a+b+c = 21

   => (a+b+c)² = 21²

   => a²+b²+c²+2(ab+bc+ca) = 441 (identity)

   => 155 + 2 (ab+bc+ca) = 441 (given)

   => ab+bc+ca = (441-155)/2

   => ab + bc + ca = 286/2

   => ab + bc + ca = 143

   Hence, our answer is 143!

   Hope you understood the method!

   Reply