the sum of two numbers is x and the product is y. what are the two numbers?

Question

the sum of two numbers is 2 and the product is 126. what are the two numbers

Answer 1

One way to approach this problem is to use system of equations.

x-first number,

y-second number.

The system:

Sum = 2;

equation is x+y=2.

Product =126,

equation is xy=126.

 

We use substitution method.

x=2-y (Equation 1)

and substitute in Equation 2:

(2-y)y=126.

2y-y²=126.

y² - 2y +126=0.

 

This quadratic equation does not have real roots. This means that the two numbers x and y are complex numbers.

Using quadratic formula and simplifying, we find that

(Try to to calculations yourself. If you have questions, please ask)

y=1-i5√5

x=1+i5√5

 

or vice-versa.