Rozwiąż równanie zawarte w załączniku ;)
x^2 - 2 ^51 *x + 2 ^100 = ( x - 2 ^50)^2
zatem
p[ x^2 - 2^51 *x + 2^100] = x - 2^50
x^2 + 2^101* x + 4^100 = ( x + 4^50 )^2
p [ x^2 + 2^101 *x + 4^100 ] = x + 4^50
czyli
p[ x^2 - 2^51* x + 2^100] - p [ x^2 + 2^101 *x + 4^100] = 2^50
I x - 2^50 I - I x + 4^50 I = 2^50
------------------------------------------
1) x < - 4^50
- x + 2^50 - ( - x - 4^50 ) = 2^50
2^50 + 4^50 = 2^50
4^50 = 0 sprzeczność
----------------------------
2) - 4^50 < x < 2^50
-x + 2^50 - x - 4^50 = 2^50
- 2x = 4^50 / : (-2)
x = - (4^50)/2
x = - (2^100)/2
x = -2^99
============
3) x > 2^50
x - 2^50 - x - 4^50 = 2^50
-2^50 - 4^50 = 2^50 sprzeczność
-----------------------------------------------
4) x = - 4^50
I - 4^50 - 2^50 I = 2^50
4^50 + 2^50 = 2^50
--------------------------------
5) x = 2^50
- I 2^50 + 4^50 I = 2^50
- 2^50 - 4^50 = 2^50
- 4^50 = 2^50 + 2^50 sprzeczność
-------------------------------------------------
Odp. x = -2^99
=================
p ( ... ) - pierwiastek kwadratowy z ( ... )
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
x^2 - 2 ^51 *x + 2 ^100 = ( x - 2 ^50)^2
zatem
p[ x^2 - 2^51 *x + 2^100] = x - 2^50
x^2 + 2^101* x + 4^100 = ( x + 4^50 )^2
zatem
p [ x^2 + 2^101 *x + 4^100 ] = x + 4^50
czyli
p[ x^2 - 2^51* x + 2^100] - p [ x^2 + 2^101 *x + 4^100] = 2^50
I x - 2^50 I - I x + 4^50 I = 2^50
------------------------------------------
1) x < - 4^50
- x + 2^50 - ( - x - 4^50 ) = 2^50
2^50 + 4^50 = 2^50
4^50 = 0 sprzeczność
----------------------------
2) - 4^50 < x < 2^50
-x + 2^50 - x - 4^50 = 2^50
- 2x = 4^50 / : (-2)
x = - (4^50)/2
x = - (2^100)/2
x = -2^99
============
3) x > 2^50
x - 2^50 - x - 4^50 = 2^50
-2^50 - 4^50 = 2^50 sprzeczność
-----------------------------------------------
4) x = - 4^50
I - 4^50 - 2^50 I = 2^50
4^50 + 2^50 = 2^50
4^50 = 0 sprzeczność
--------------------------------
5) x = 2^50
- I 2^50 + 4^50 I = 2^50
- 2^50 - 4^50 = 2^50
- 4^50 = 2^50 + 2^50 sprzeczność
-------------------------------------------------
Odp. x = -2^99
=================
p ( ... ) - pierwiastek kwadratowy z ( ... )