Question

if a square + b square + c square = 90 and a + b + c = 20 then find the value of AB + BC + CA​

Answer 1

Answer:

$\large (ab+bc+ca)=155$

Step-by-step explanation:

Given :

$\large a^2+b^2+c^2=90 \ ..(i)$

a + b + c = 20  ... ( ii )

Using identity here

$\large (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\\\\\\\large \text{Rewrite as }\\\\\\\large 2(ab+bc+ca)=(a+b+c)^2-(a^2+b^2+c^2)$

Now put value from ( i )  and  ( ii ) we get

$\large 2(ab+bc+ca)=(20)^2-(90)\\\\\\\large 2(ab+bc+ca)=400-90\\\\\\\large 2(ab+bc+ca)=310\\\\\\\large (ab+bc+ca)=155$

Thus we get answer 155.