<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
8x + 5y = 18 ------- eqn 1
6x + y = -2 -------- eqn 2
Multiply eqn 2 by -5
-30x -5y = 10 ----- eqn 3
Add eqn 1 and eqn 3 so that y terms gets eliminated
8x + 5y = 18
-30x -5y = 10
( + ) --------------
-22x = 28
Divide both sides by -22
Substitute the x value in eqn 1
Answer:
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.
Step-by-step 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
these options correspond to a and b from the original question.