Question

if a+b+c= 12 and a^2+b^2+c^2=100 find the value of ab+bc+ca​

Answer 1

$(ab + bc + ca ) =22$

Answer 2

Answer:

The answer will be 22.

Step-by-step explanation:

Given,

a+b+c= 12; (i)

a^2+b^2+c^2=100; (ii)

Square both side in eq. (i);

(a+b+c)^2 = (12)^2;

a^2+b^2+c^2 + 2ab+2bc+2ca = 144; (since, (a+b+c)^2 = a^2+b^2+c^2 + 2ab+2bc+2ca)

100 + 2ab+2bc+2ca = 144; (from eq. (ii))

2ab+2bc+2ca = 44;

2(ab+bc+ca) = 44;

ab+bc+ca = 22;

That's all.