Question

If a+b+c=7 and ab+bc+ca=20, find the value of a^2+b^2+c^2.​

Answer 1

Answer: a²+b²+c²= 9

Step-by-step explanation:

Given- a+b+c= 7

ab+bc+ca= 20

To find- value of a²+b²+c²

Solution- a+b+c= 7 (Given)

Squaring both sides

(a+b+c)² = 7²

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

So, using this algebraic identity, we will solve the given question.

(a+b+c)² = 7²

⇒a²+b²+c²+2ab+2bc+2ca= 49

⇒a²+b²+c²+2(ab+bc+ca)= 49 [Taking 2 as common]

⇒a²+b²+c²+2(20)= 49 [∵ ab+bc+ca= 20 (Given)]

⇒a²+b²+c²+40= 49

⇒a²+b²+c²= 49-40 [Transposing]

⇒a²+b²+c²= 9

Hence, a²+b²+c²= 9