Question

V_a +V_b= 22.222 and V_a^2+V_b^2=147.15

How do you get V_a and V_b?

Answer 1

V_a +V_b= 22.222 ---(1)

V_a^2+V_b^2=147.15 ---(2)

From equation (2) we can write (V_a + V_b)^2 = V_a^2+V_b^2 - 2V_a*V_b

V_a^2+V_b^2 = (V_a + V_b)^2 + 2V_a*V_b

Plug the given values : 147.15 = (22.22)^2 + 2*V_aV_b

V_a*V_b = - 173.289 ----(3)

V_b = -173.289/V_a

Now use equation (1) and (3) to solve for V_a and V_b

V_a -173.289/V_a = 22.22

V_a^2 - 22.22V_a - 173.289 =0

Solve the quadartic equation solver to get values of V_a:

V_a = 28.33 and V_a = -6.11

V_b = 22.22 - 28.33 = -6.11 and V_b = 22.22 +6.11 = 28.33