Question

Solve this please .......​

Answer 1

The sum of reciprocals is 2/3.

You don't need complex numbers to solve this, but if you try to find a and b you will need complex numbers.

Explanation:

a+b = 2

a*b = 3

1/a + 1/b = x

(a*b)*(1/a + 1/b) = (a*b)x

b + a = (a*b)(x)

2 = 3x

x = 2/3

b = 2 - a

a*(2 - a) = 3

-a^2 + 2a = 3

-a^2 + 2a - 3 = 0

a^2 - 2a + 3 = 0

let's solve the quadratic equation

a^2 - 2a + 3 = a^2 - 2a + 1 + 2 = (a - 1)^2 + 2 = 0

(a - 1)^2 = -2

`a_1 - 1 = √(2)i\\a_1 = 1+√(2)i\\\\a_2 - 1 = -√(2)i\\a_2 = 1 - √(2)i\\`

these options correspond to a and b from the original question.