What two numbers can be multiplied to get 21, and added to get - 2?

Xy=21

x+y=-2 ⇒x=-2-y

We solved this equation system by substitution method.

(-2-y) y=21

-2y-y²=21

y²+2y+21=0

We solved this square equation:

y=[-2⁺₋√ (4-84) ]/2

y=[-2⁺₋√-80] / 2

y = (-2⁺₋4√-5) / 2

y=-1⁺₋2√5 i

Therefore.

y₁=-1-2√5 i ⇒ x₁=-2-y=-1+2√5 i

y₂=-1+2√5 i ⇒ x₂=-2-y=-1-2√5 i

Solution: we have two solution.

Solution₁

x₁=-1+2√5 i; y₁=-1-2√5 i

And the other solution is:

solution ₂

x₂=-1+2√5 i; y₂=-1-2√5 i

To check:

Solution₁

(-1+2√5 i) (-1-2√5 i) = 1+2√5 i-2√5 i+20=21

(-1+2√5 i) + (-1-2√5 i) = - 2

Solution₂

(-1-2√5 i) (-1+2√5 i) = 1-2√5 i+2√5 i+20=21

(-1-2√5 i) + ((-1+2√5 i) = - 2

Therefore:

the solution are complex numbers.

A number is : (-1-2√5 i) and the other number is (-1+2√5 i)

Remember:

i=√-1