CPhill

OK, Leo....!!!!

x^2 + y^2 + 2x - 4y - 8      complete the square on x and y

x^2 +2x + 1  + y^2 - 4y + 4   - 1   - 4      factor

(x + 1)^2   + (y - 2)^2   -   5

The minimum value of  -5    will be  achieved when x = -1  and y  = 2

See my answer here:

 https://web2.0calc.com/questions/help_9450

The difference of  8 and 9  =     

8  - 9  = 

8 + (-9)

Let the roots  be   x, y , z

So

 [ log  ₂ x  +  log ₂  y  + log ₂  z ]  = 5

 log ₂  (xyz)  = 5

2^5  = xyz

xyz  = 32

And the  product of the  roots =  -a/ 8

xyz  = -a / 8

32 = -a / 8

256 = - a

a  = -256

Here : https://web2.0calc.com/questions/3d-geometry-please-help

Hey....that sounds like a ot of fun.....(except the  mosquito part )

True.....

Very nice, hureka!!!!

No prob...!!!!