Question

If ab+bc+ca= 12 and a^2+b^2+c^2= 64 then find a+b+c

Answer 1

Answer:

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

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

(a+b+c)^2=64+2.12=64+24=88

a+b+c=√88=√4.22=2√22

Answer 2

Answer:

2√22

Step-by-step explanation:

Given

ab + bc + ca = 12

a² + b² + c² = 64

We know that

(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)

⇒(a + b + c)² = 64 + 2*(12)

                     = 64 + 24

                     = 88

⇒ a + b + c = √88 = √(4*22)

∴ a + b + c = 2√22