Question

two numbers that multiplies to -114 and adds up to -1?

Answer 1

Solve the system:
\[-114=x*y, -1=x+y\]

Answer 2

i have no clue

Answer 3

\[-114 = y(-y-1) \rightarrow y ^{2}+y-114 = 0\]Using the quadratic formula we get:
\[y _{1} = (1/2 )(-1-\sqrt457 )\]\[y_{2}=(1/2)(-1+\sqrt457)\]
Using those we can now solve for x:
\[-1 = x_{1} + y_{1} \rightarrow -1 = x_{1} + (1/2 )(-1-\sqrt457 ) \rightarrow x_{1} = (1/2)(-1+\sqrt457) \]\[-1 = x_{2} + y_{2} \rightarrow -1 = x_{2} + (1/2)(-1+\sqrt457) \rightarrow x_{2} = (1/2)(-1-\sqrt457) \]
As you can see \[x_{1} = y_{2}, x_{2} = y_{1}\]
This gives us one possible soulution:
\[(1/2)(-1+\sqrt457) * (1/2)(-1-\sqrt457) = -114 \]\[(1/2)(-1+\sqrt457) + (1/2)(-1-\sqrt457) = -1 \]