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Mathematics
1 March, 05:15
What two numbers multiply to - 96 and add to 7
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Jordon Morton
1 March, 05:27
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The numbers are x and y.
Therefore, we can suggest this system of equations:
xy=-96
x+y=7 ⇒x=7-y
solve this systeme by substitution method.
(7-y) y=-96
7y-y²=-96
y²-7y-96=0
We solve this square ecuation:
y=[7⁺₋√ (49-4 (1) (-96)) ] / 2 = (7⁺₋√433) / 2
We have two solutions:
y₁ = (7-√433) / 2 (y₁≈-6.904326 ...)
x₁=7-y₁
x₁=7 - (7-√433) / 2 = (7+√433) / 2 (x₁≈13.904326 ...)
y₂ = (7+√433) / 2 (y₂≈13.904326 ...)
x₂=7-y₂
x₂=7 - (7+√433) / 2 = (7-√433) / 2 (x₂≈-6.904326 ...)
Therefore:
The numbers are (7-√433) / 2 and (7+√433) / 2.
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