If a+b+c=root(42) and a2+b2+c2=16 . . .

Question : If a+b+c=√42 and a²+b²+c²=16, then find the value of ab+bc+ca

Doubt by Parth 

Solution : 

a+b+c=√42 — (1) 

a²+b²+c²=16 — (2) 

We know, 
(a+b+c)²=a²+b²+c²+2ab+2bc+2ca
(√42)²=16+2(ab+bc+ca)
42=16+2(ab+bc+ca)
42-16=2(ab+bc+ca)

26=2(ab+bc+ca)
26/2=(ab+bc+ca)
13=ab+bc+ca

Hence, the value of ab+bc+ca=13