Question

What two numbers add to 9 but multiply to -42

Answer 1

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

Answer 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.