Question

If a+b+c=10; aa+bb+cc=30. find value of ab+bc+ ca=?

Answer 1

we have formula

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

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

Now substitute the given values in the above equation.
(10)2 - (30) = 2(ab+bc+ca)
100-30=2(ab+bc+ca)
70=2(ab+bc+ca)
70/2=(ab+bc+ca)
Therefore ab+bc+ca=35