Question

If a^2+b^2=25 and ab+bc+ca=3, find a+b+c.

Answer 1

Given a^2 + b^2 + c^2 = 25 and ab + bc + ca = 3.

Now,

We know that (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

                                             = 25 + 2(ab + bc + ca)

                                             = 25 + 2(3)

                                             = 31.


(a + b + c) = $\sqrt{31}$


Hope this helps!

Answer 2

a^2 + b^2 + c^2 =25

ab+bc+ca=3

(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)

⇒ (a+b+c)^2 = 25+ 2(3)


⇒ (a+b+c)^2 = 25+6

⇒ (a+b+c)^2 = 31

⇒ a+b+c = \pm± √31