# Z9–I–1 2018 čísla

```#0  xxx() called at [/LinSys.php:671]
#1  LinSys::tryIntegerEquations(Array ([0] => x,[1] => y), Array ([0] =>  4 * (1/x + 1/y )  = 4 * (  1/4 ) ), 1) called at [/LinSys.php:344]
#2  LinSys::SolveInner(1/x + 1/y = 1/4
x>0
y>0, , 1, linsys, 1, , 1, 1) called at [/LinSys.php:220]
#3  LinSys::Solve(1/x + 1/y = 1/4
x>0
y>0, , 1, linsys, 1, , 1) called at [/Example_Generic.php:87]
#4  Example_Generic->GenerateSolveVector(stdClass Object ([example_id] => 7040,[title_sk] => Z9–I–1 2018 čísla,[title_en] => ,[title_cz] => Z9–I–1 2018 čísla,[add_date] => 2018-10-18 14:17:45,[img] => hyperbola_1.jpg,[visible] => 1,[text_sk] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:
1/x + 1/y = 1/4 .,[text_en] => ,[text_cz] => Najděte všechna kladná celá čísla x a y, pro která platí:

1/x + 1/y = 1/4,[input_vector] => ,[output_vector] => \$x1="x1=##@x + y = 1/4xy
@4x+4y = xy

@x1=5, y1=20
@x2=6, y2=12
@x3=8, y3=8
@x4=12, y4=6
@x5=20, y5=5
x1 = 5";
\$y1="y1=##y1=fr(1,1/4 - 1/x1)";
\$y1_inteqs="1/x + 1/y = 1/4
x>0
y>0";,[user_id] => 12,[approved] => 1,[cnt_views] => 1997,[cnt_solved] => 1176,[cnt_solved_ok] => 116,[focus] => 1,[preview_sk] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:  1/x + 1/y = 1/4 .,[preview_en] => ,[preview_cz] => Najděte všechna kladná celá čísla x a y, pro která platí:  1/x + 1/y = 1/4,[preview_vector_sk] => ,[preview_vector_en] => ,[preview_vector_cz] => ,[last_regenerate] => 2019-07-11 15:12:20,[external_url] => ,[suggestion_id] => 10211,[fulltext_sk] => ~ z9 i 1 2018 cisla najdite vsetky kladne cele x a y pre ktore plati 1 + = 4 rovnica algebra celociselna nepriama umera zakladne funkcie matematicka olympiada 9 rocnik stredna skola 7040 ~,[fulltext_en] => ~ 7040 ~,[fulltext_cz] => ~ z9 i 1 2018 cisla najdete vsechna kladna cela x a y pro ktera plati 1 + = 4 rovnice algebra celociselna neprima umera zakladni funkce matematicka olympiada 9 rocnik stredni skola 7040 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Z9–I–1 2018 čísla,[text] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:
1/x + 1/y = 1/4 .), ) called at [/Example_Generic.php:869]
#5  Example_Generic->Run(stdClass Object ([example_id] => 7040,[title_sk] => Z9–I–1 2018 čísla,[title_en] => ,[title_cz] => Z9–I–1 2018 čísla,[add_date] => 2018-10-18 14:17:45,[img] => hyperbola_1.jpg,[visible] => 1,[text_sk] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:
1/x + 1/y = 1/4 .,[text_en] => ,[text_cz] => Najděte všechna kladná celá čísla x a y, pro která platí:

1/x + 1/y = 1/4,[input_vector] => ,[output_vector] => \$x1="x1=##@x + y = 1/4xy
@4x+4y = xy

@x1=5, y1=20
@x2=6, y2=12
@x3=8, y3=8
@x4=12, y4=6
@x5=20, y5=5
x1 = 5";
\$y1="y1=##y1=fr(1,1/4 - 1/x1)";
\$y1_inteqs="1/x + 1/y = 1/4
x>0
y>0";,[user_id] => 12,[approved] => 1,[cnt_views] => 1997,[cnt_solved] => 1176,[cnt_solved_ok] => 116,[focus] => 1,[preview_sk] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:  1/x + 1/y = 1/4 .,[preview_en] => ,[preview_cz] => Najděte všechna kladná celá čísla x a y, pro která platí:  1/x + 1/y = 1/4,[preview_vector_sk] => ,[preview_vector_en] => ,[preview_vector_cz] => ,[last_regenerate] => 2019-07-11 15:12:20,[external_url] => ,[suggestion_id] => 10211,[fulltext_sk] => ~ z9 i 1 2018 cisla najdite vsetky kladne cele x a y pre ktore plati 1 + = 4 rovnica algebra celociselna nepriama umera zakladne funkcie matematicka olympiada 9 rocnik stredna skola 7040 ~,[fulltext_en] => ~ 7040 ~,[fulltext_cz] => ~ z9 i 1 2018 cisla najdete vsechna kladna cela x a y pro ktera plati 1 + = 4 rovnice algebra celociselna neprima umera zakladni funkce matematicka olympiada 9 rocnik stredni skola 7040 ~,[english_last_modified] => 0000-00-00 00:00:00,[title] => Z9–I–1 2018 čísla,[text] => Nájdite všetky kladné celé čísla x a y, pre ktoré platí:
1/x + 1/y = 1/4 .)) called at [/index_real.php:185]
#6  HackMath->ExampleDetail() called at [/index_real.php:316]
#7  HackMath->ExampleAction() called at [/index_real.php:461]
#8  HackMath->Run() called at [/index_real.php:815]
#9  include(/index_real.php) called at [/index.php:41]
```