What 2 numbers multiplied together equal 54 and added together equal 6?

Answer 1

There are no two real numbers that do, but two complex numbers that do are: (3 + i√45) and (3 - i√45).

If the numbers multiply to -54 and sum to 6, then two numbers that do are: (3 + √63) ≈ 10.937 and (3 - √63) ≈ -4.937

If the numbers multiply to -54 and sum to -6, then two numbers that do are: (-3 + √63) ≈ 4.937 and (-3 - √63) ≈ -10.937

Answer 2

Let the numbers by 'm' & 'n'

Hence

m + n = 6

mn = 54

Let n = 54/n

Substitute

m + 54/m = 6

Multiply through by 'm'

m^2 + 54 = 6m

Form a quadratic equation

m^2 - 6m + 54 = 0

This will not factor

So use Quadratic Equa'n

m = { - - 6 +/-sqrt[(-6)^2 - 4(1)(54)]} / 2(1)

m = { 6 +/- sqrt(36 -216]} / 2

m = { 6 +/- sqrt[-180} /2

Since we cannot find the square root of a negative number, then the answer is unresolved, unles wee move into IMAGINARY NNumbers.

Hence sqrt(-180) = sqrt(-1) X sqrt(180)

The square root of '-1' is defined as 'i'.

Sqrt(180) = +/-13.4164....

Hence

m = {6 +/- 13.4164i } / 2

M = 3 +/- 6.7082 i

or for clarity

m = 3 + 6.7082 i & 3 - 6.7082 i .