Answer:
a = -1 + √257 and b = -1 - √257
Step-by-step explanation:
consider two numbers a and b ,where :
a + b = -2
a × b = -256
Then
b = -a -2
a × b = -256
Then
b = -a -2
a × (-a -2) = -256
Then
b = -a -2
-a² -2a = -256
Then
b = -a -2
a² + 2a - 256 = 0
Solving the equation:
a² + 2a - 256 = 0
The discriminant ∆ = 2² - 4(1)(-256) = 1028
Then
[tex]a = \frac{-2+\sqrt{1028} }{2} = -1 + \sqrt{257}[/tex]
Or
[tex]a = \frac{-2-\sqrt{1028} }{2} = -1 - \sqrt{257}[/tex]
Then
b = 1 - √257 - 2 = -1 - √257
Or
b = -1 + √257
