Question

a+b+c=9 ab+bc+ca=23 so a²+b²+c²=​

Answer 1

We know that,

(a+b+c)² = a²+b²+c²+2ab+2bc+2ac

Given, a+b+c=9 and ab+bc+ac=23.

So,

(a+b+c)² = a²+b²+c²+2ab+2bc+2ac

or, (9)² = a²+b²+c²+2(ab+bc+ac)

or, 81 = a²+b²+c²+2(23)

or, 81 = a²+b²+c²+46

or 81 - 46 = a²+b²+c²

or, 35 = a²+b²+c²

Answer:

a²+b²+c² = 35 .