What two numbers add to 9 but multiply to - 42

Hi,

x+y = 9 ⇒ x = 9-y

x·y = - 42

(9-y) ·y = - 42

9y-y² = - 42

y²-9y-42 = 0 for a = 1, b = - 9 e c = - 42

Δ = b²-4ac

Δ = (-9) ²-4 (1) (-42)

Δ = 81+168

Δ = 249

y₁ = (-b+√Δ) / 2a = ( - (-9) + √249) / 2 (1) = (9+√249) / 2 = 9/2 + √249/2

y₂ = (-b-√Δ) / 2a = ( - (-9) - √249) / 2 (1) = (9-√249) / 2 = 9/2 - √249/2

For y = 9/2 + √249/2

x+y = 9

x = 9-y

x = 9 - (9/2 + √249/2)

x = 9/2 - √249/2

For y = 9/2 - √249/2

x+y = 9

x = 9-y

x = 9 - (9/2 - √249/2)

x = 9/2 + √249/2

Answer:

Numbers: 9/2 + √249/2 and 9/2 - √249/2

The factors of 42 are 1,42,2,21,3,14,6,7. Non of these add together to get 9. One would have to be positive and the other negative but it still doesn't work.