Question

Given ab+bc-ca = 3 and a^{​​​​​​2}+b^{​​​​​​2}+c^{​​​​​​2} = 31
Then find the value of (a-b+c)

Answer 1

(a-b+c)^2 = a^{​​​​​​2}+b^{​​​​​​2}+c^{​​​​​​2} - 2(ab+bc-ca)
= 31 - 2*3 = 31-6 = 25

(a-b+c)^2 = 25

a-b+c = 5 or -5