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What two numbers add to 9 but multiply to -42

2 Answers

2 votes
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

User Jeson Martajaya
by
8.0k points
1 vote
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.
User Yanni Wang
by
8.4k points

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