Question

If a+b+c=7 and ab +bc+ca=20,find the value of a2+b2+c2

Answer 1

(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

a²+b²+c²= (a+b+c)²-2ab-2bc-2ca

a²+b²+c²= (7)²-2(ab+bc+ca) a²+b²+c².

= (7)²-2(20) a²+b²+c²

= 49-40 a²+b²+c²= 9

hence answer =9

Answer 2

$\Large\boxed{ANSWER={a}^{2}+{b}^{2}+{c}^{2}=9}}}}}}}$

$\Large\boxed{Step\: by\: step\: explanation}$

Using

(a+b+c)² formula

(a+b+c)²=a²+b²+c²+2ab+2bc+2ac

(a+b+c)²-2ab-2bc-2ac=a²+b²+c²

(7)²-2(ab+bc+ac)=a²+b²+c²

49-2(20)=a²+b²+c²

therefore, a²+b²+c²=9

$\Large\boxed{Solved}$