What two numbers multiply to get 21 but add to get 2?

Question

I am doing diamond problem for algebra 1 and I need help with the diamond part what multiplies to get 21 but adds to get 2

Answer 1

If x and y are two unknown numbers, then you have to solve the sytem of equations:

x+y=2

xy=21

 

By substitution, from the first equation y=2-x, plug in into the second one

x(2-x)=21

x²-2x+21=0

It is clear that this equation has no real roots; you can write if as

(x-1)²=-20,

which is not true in the set of real number. If you need solution in the set of complex numbers, you can continue.