CPhill

Simplify as

x^2 + (17 - m)x + 4  = 0

If we have two distinct roots  then the discriminant is > 0

So

(17- m)^2 - 4*4  >  0

(17 - m)^2  > 16      take both roots

17  - m  > 4           17 - m <  -4

 13 > m                  21 < m

m  comes  from (-inf , 13) U ( 21, inf)

https://web2.0calc.com/questions/regular-hexagon

Pythagorean Theorem

(r - 10)^2  + ( r -13)^2  = r^2      simplify

2r^2 - 46r + 269  = r^2

r^2 - 46r + 269  = 0

r^2 -46r  + 529  = -269 + 529

(r - 23)^2  = 260      take the positive root

r - 23 = sqrt 260

r - 23  =   2sqrt 65

r = 2sqrt 65 + 23 ≈ 39.125

Case 1

x = 0  and  one  of the other variables = 2  →  5 different solutions

Case 2

x = 0   and two of the other variables = 1  →  C(5,2)  = 10 different solutions

Case 3

x = 1   and one  of the other variables = 1 →  C(5,1)  = 5 different solutions

5 + 10 + 5  =     20 possible solutions

The width of the square = 1 + 1 + 1/2 = 2.5

width  = the height

So

Area  = 2.5^2  =  6.25

And the question is ????

No question here.....

Mmm...OK....

You may not use a calculator....but I will  !!!!

0.4482758620689655172413793103^_ (period 28)

2/131

This is a  repeating  decimal with a period of 130

0.015267175572519083969465648854961832061068702290076335^_\
87786259541984732824427480916030534351145038167938931297^_\
70992366412213740458^_
(period 130)