Question

If a+b+c=8 and ab+bc+cd=19 , find a^2+b^2+c^2.

Answer 1

I think there is a mistake in typing (ab+bc+ca), you have written cd

(a+b+c)=8

Square on both sides,

(a+b+c)²=8²

a²+b²+c²+2(ab+bc+ca) =64

a²+b²+c²+2*19=64

a²+b²+c²=64-38

a²+b²+c²=26

Answer 2

It should be ab+bc+cd instead of ab+bc+cd we know,
(a+b+c)² = a²+b²+c²+2(ab+bc+cd)
Using this identity let's solve, putting values we get,
(8)²= a²+b²+c²+2(19)

64= a²+b²+c²+38

64-38 = a²+b²+c²

a²+b²+c²= 26<------ Answer

hope this helps you