The most recent revision of non-linear case of task 18 in EGE Informatics vs Standard aproach to solve 18-th in EGE Mathematics

Consider problem 7 from recent presentation  posted at
http://kpolyakov.spb.ru/school/ege.htm
Линейное (и нелинейное) программирование в задаче 18 ЕГЭ по информатике 

  

Now detect A like we manage to get the job done
working on problems 18-th of EGE Mathematics

f1(x) =(x-A)^2 + 10
f2(x) = -x^2/4 + 30

System 1

(1) f1(x) = f2(x)
(2) df1(x)/dx= df2(x)/dx

Getting derivatives:-

df1(x)/dx = 2(x-A)
df2(x)/dx = -x/2

First:-  Solve (2)

2(x-A) = -x/2
(5/2)x = 2*A
x = (4/5)*A

Second:-  Solve (1)

((4/5)A -A)^2 + 10 =  (-1/4)*(16/25)*A^2 + 30
(-1/5)^2*A^2 +10  =  (-1/4)*(16/25)*A^2 + 30
((1/25)+(4/25))*A^2 = 20
(1/5)*A^2 = 20

Here we go :-

A^2 = 100
A= |100^(1/2)| = 10

Would I skip original declaration in header, new revision (non-linear) of 18 -th EGE Informatics would look pretty much like 18-th in EGE Mathematics having average level of difficulty.
Obviously complexity of non-linear revision of 18-th EGE Informatics might be significantly increased  when it would be designed for real EGE exam. 
1)  Make skiils set to build area colored gray on second snapshot requiring
     boolean algebra in depth knowledge.
2)  Good background in differential geometry, specifically touch of curves related

Condition D=0 works only for parabolic curves.  Method applied above has
universal nature. See for instance

 See also other samples at http://www.math24.ru/%D1%81%D0%BE%D0%BF%D1%80%D0%B8%D0%BA%D0%BE%D1%81%D0%BD%D0%BE%D0%B2%D0%B5%D0%BD%D0%B8%D0%B5-%D0%BF%D0%BB%D0%BE%D1%81%D0%BA%D0%B8%D1%85-%D0%BA%D1%80%D0%B8%D0%B2%D1%8B%D1%85.html