Question

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

Answer 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!!

Answer 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!