פתיחת התפריט הראשי
דף הבית
אקראי
בסביבה
כניסה לחשבון
הגדרות
תרומה לוויקיספר
אודות ויקיספר
הבהרות משפטיות
חיפוש
מתמטיקה תיכונית/אלגברה תיכונית/משוואות/משוואות ריבועיות/תרגילים/נוסחת השורשים ג
שפה
מעקב
עריכה
<
מתמטיקה תיכונית
|
אלגברה תיכונית
|
משוואות
|
משוואות ריבועיות
|
תרגילים
נוסחת השורשים - תרגילים
עריכה
פתרו את המשוואות הבאות בעזרת נוסחת השורשים, או בכל דרך אחרת. מותר להשתמש במחשבון.
5
x
2
−
5
x
−
2929
12
=
−
1
3
{\displaystyle 5x^{2}-5x-{\frac {2929}{12}}=-{\frac {1}{3}}}
25
13
x
2
−
47
60
x
−
306
11
=
12
13
x
2
−
13
4
x
+
2
11
{\displaystyle {\frac {25}{13}}x^{2}-{\frac {47}{60}}x-{\frac {306}{11}}={\frac {12}{13}}x^{2}-{\frac {13}{4}}x+{\frac {2}{11}}}
5
x
2
+
123
2
x
−
1615
2
=
9
x
{\displaystyle 5x^{2}+{\frac {123}{2}}x-{\frac {1615}{2}}=9x}
1
4
x
2
+
149
22
x
−
161
3
=
−
3
4
x
2
−
8
11
x
+
1
3
{\displaystyle {\frac {1}{4}}x^{2}+{\frac {149}{22}}x-{\frac {161}{3}}=-{\frac {3}{4}}x^{2}-{\frac {8}{11}}x+{\frac {1}{3}}}
5
x
2
−
275
21
x
−
2649
70
=
−
7
10
{\displaystyle 5x^{2}-{\frac {275}{21}}x-{\frac {2649}{70}}=-{\frac {7}{10}}}
7
x
2
+
105
4
x
+
763
52
=
−
14
13
{\displaystyle 7x^{2}+{\frac {105}{4}}x+{\frac {763}{52}}=-{\frac {14}{13}}}
3
x
2
+
1
5
x
−
41
=
−
7
5
{\displaystyle 3x^{2}+{\frac {1}{5}}x-41=-{\frac {7}{5}}}
x
2
+
1
2
x
−
103
9
=
−
2
{\displaystyle x^{2}+{\frac {1}{2}}x-{\frac {103}{9}}=-2}
6
x
2
+
10134
91
x
+
9813
56
=
−
12
13
x
+
3
8
{\displaystyle 6x^{2}+{\frac {10134}{91}}x+{\frac {9813}{56}}=-{\frac {12}{13}}x+{\frac {3}{8}}}
6
x
2
−
101
7
x
+
148
7
=
4
x
+
7
{\displaystyle 6x^{2}-{\frac {101}{7}}x+{\frac {148}{7}}=4x+7}
14
5
x
2
+
743
70
x
+
201
40
=
−
6
5
x
2
+
3
14
x
−
11
8
{\displaystyle {\frac {14}{5}}x^{2}+{\frac {743}{70}}x+{\frac {201}{40}}=-{\frac {6}{5}}x^{2}+{\frac {3}{14}}x-{\frac {11}{8}}}
x
2
+
33
10
x
+
56
15
=
7
3
{\displaystyle x^{2}+{\frac {33}{10}}x+{\frac {56}{15}}={\frac {7}{3}}}
4
x
2
−
226
5
x
+
486
5
=
2
{\displaystyle 4x^{2}-{\frac {226}{5}}x+{\frac {486}{5}}=2}
6
x
2
−
150
7
x
+
285
14
=
3
2
{\displaystyle 6x^{2}-{\frac {150}{7}}x+{\frac {285}{14}}={\frac {3}{2}}}
3
x
2
+
303
10
x
+
386
5
=
7
{\displaystyle 3x^{2}+{\frac {303}{10}}x+{\frac {386}{5}}=7}
68
11
x
2
+
769
21
x
−
302
11
=
−
9
11
x
2
−
5
7
x
+
6
11
{\displaystyle {\frac {68}{11}}x^{2}+{\frac {769}{21}}x-{\frac {302}{11}}=-{\frac {9}{11}}x^{2}-{\frac {5}{7}}x+{\frac {6}{11}}}
5
x
2
+
927
28
x
+
393
7
=
−
9
14
x
+
8
7
{\displaystyle 5x^{2}+{\frac {927}{28}}x+{\frac {393}{7}}=-{\frac {9}{14}}x+{\frac {8}{7}}}
49
12
x
2
+
298
63
x
−
29
=
13
12
x
2
+
13
9
x
−
5
7
{\displaystyle {\frac {49}{12}}x^{2}+{\frac {298}{63}}x-29={\frac {13}{12}}x^{2}+{\frac {13}{9}}x-{\frac {5}{7}}}
22
7
x
2
−
73
4
x
+
671
40
=
1
7
x
2
−
x
−
1
10
{\displaystyle {\frac {22}{7}}x^{2}-{\frac {73}{4}}x+{\frac {671}{40}}={\frac {1}{7}}x^{2}-x-{\frac {1}{10}}}
3
x
2
+
40
7
x
+
1203
91
=
−
8
x
−
12
13
{\displaystyle 3x^{2}+{\frac {40}{7}}x+{\frac {1203}{91}}=-8x-{\frac {12}{13}}}
3
x
2
+
971
12
x
+
1817
4
=
−
1
12
x
−
7
4
{\displaystyle 3x^{2}+{\frac {971}{12}}x+{\frac {1817}{4}}=-{\frac {1}{12}}x-{\frac {7}{4}}}
7
x
2
−
581
15
x
+
311
6
=
1
2
{\displaystyle 7x^{2}-{\frac {581}{15}}x+{\frac {311}{6}}={\frac {1}{2}}}
x
2
+
5
x
+
69
20
=
−
9
5
{\displaystyle x^{2}+5x+{\frac {69}{20}}=-{\frac {9}{5}}}
7
x
2
−
14
x
−
59
3
=
4
3
{\displaystyle 7x^{2}-14x-{\frac {59}{3}}={\frac {4}{3}}}
x
2
+
57
14
x
+
29
35
=
3
14
x
+
7
5
{\displaystyle x^{2}+{\frac {57}{14}}x+{\frac {29}{35}}={\frac {3}{14}}x+{\frac {7}{5}}}
x
2
−
1
7
x
+
11
14
=
−
x
+
11
14
{\displaystyle x^{2}-{\frac {1}{7}}x+{\frac {11}{14}}=-x+{\frac {11}{14}}}
2
x
2
−
52
x
+
1681
5
=
−
9
5
{\displaystyle 2x^{2}-52x+{\frac {1681}{5}}=-{\frac {9}{5}}}
25
12
x
2
−
257
35
x
−
22
49
=
1
12
x
2
−
1
5
x
−
6
{\displaystyle {\frac {25}{12}}x^{2}-{\frac {257}{35}}x-{\frac {22}{49}}={\frac {1}{12}}x^{2}-{\frac {1}{5}}x-6}
89
13
x
2
+
33
20
x
−
313
65
=
−
2
13
x
2
+
2
x
−
8
13
{\displaystyle {\frac {89}{13}}x^{2}+{\frac {33}{20}}x-{\frac {313}{65}}=-{\frac {2}{13}}x^{2}+2x-{\frac {8}{13}}}
3
x
2
−
3
4
x
−
311
4
=
1
{\displaystyle 3x^{2}-{\frac {3}{4}}x-{\frac {311}{4}}=1}
x
2
−
19
5
x
+
37
5
=
5
{\displaystyle x^{2}-{\frac {19}{5}}x+{\frac {37}{5}}=5}
28
11
x
2
+
26
x
+
139
7
=
−
5
11
x
2
−
1
4
x
+
13
7
{\displaystyle {\frac {28}{11}}x^{2}+26x+{\frac {139}{7}}=-{\frac {5}{11}}x^{2}-{\frac {1}{4}}x+{\frac {13}{7}}}
x
2
−
220
21
x
+
271
21
=
−
2
x
−
2
3
{\displaystyle x^{2}-{\frac {220}{21}}x+{\frac {271}{21}}=-2x-{\frac {2}{3}}}
3
x
2
+
3
x
−
88
13
=
−
10
13
{\displaystyle 3x^{2}+3x-{\frac {88}{13}}=-{\frac {10}{13}}}
x
2
+
463
10
x
−
247
5
=
13
10
x
+
3
5
{\displaystyle x^{2}+{\frac {463}{10}}x-{\frac {247}{5}}={\frac {13}{10}}x+{\frac {3}{5}}}
2
x
2
−
1
7
x
+
8
11
=
x
+
8
11
{\displaystyle 2x^{2}-{\frac {1}{7}}x+{\frac {8}{11}}=x+{\frac {8}{11}}}
x
2
−
55
3
x
+
328
15
=
−
4
5
{\displaystyle x^{2}-{\frac {55}{3}}x+{\frac {328}{15}}=-{\frac {4}{5}}}
x
2
+
8
5
x
−
2132
225
=
13
9
{\displaystyle x^{2}+{\frac {8}{5}}x-{\frac {2132}{225}}={\frac {13}{9}}}
7
5
x
2
+
99
7
x
−
122
3
=
−
3
5
x
2
−
13
7
x
−
2
3
{\displaystyle {\frac {7}{5}}x^{2}+{\frac {99}{7}}x-{\frac {122}{3}}=-{\frac {3}{5}}x^{2}-{\frac {13}{7}}x-{\frac {2}{3}}}
25
9
x
2
+
106
5
x
+
175
4
=
−
2
9
x
2
−
9
5
x
+
1
{\displaystyle {\frac {25}{9}}x^{2}+{\frac {106}{5}}x+{\frac {175}{4}}=-{\frac {2}{9}}x^{2}-{\frac {9}{5}}x+1}
4
x
2
+
295
14
x
−
146
11
=
−
13
14
x
−
14
11
{\displaystyle 4x^{2}+{\frac {295}{14}}x-{\frac {146}{11}}=-{\frac {13}{14}}x-{\frac {14}{11}}}
4
x
2
+
8
x
+
181
49
=
1
{\displaystyle 4x^{2}+8x+{\frac {181}{49}}=1}
6
x
2
−
72
x
+
793
12
=
1
12
{\displaystyle 6x^{2}-72x+{\frac {793}{12}}={\frac {1}{12}}}
79
11
x
2
−
8
x
−
341
5
=
13
11
x
2
+
4
x
−
7
10
{\displaystyle {\frac {79}{11}}x^{2}-8x-{\frac {341}{5}}={\frac {13}{11}}x^{2}+4x-{\frac {7}{10}}}
2
x
2
+
14
3
x
−
10
3
=
−
x
{\displaystyle 2x^{2}+{\frac {14}{3}}x-{\frac {10}{3}}=-x}
6
x
2
+
167
x
+
5684
5
=
−
13
x
+
14
5
{\displaystyle 6x^{2}+167x+{\frac {5684}{5}}=-13x+{\frac {14}{5}}}
7
x
2
+
49
2
x
+
133
8
=
−
7
8
{\displaystyle 7x^{2}+{\frac {49}{2}}x+{\frac {133}{8}}=-{\frac {7}{8}}}
5
x
2
+
25
14
x
−
233
182
=
−
12
13
{\displaystyle 5x^{2}+{\frac {25}{14}}x-{\frac {233}{182}}=-{\frac {12}{13}}}
4
x
2
+
48
x
+
5
2
=
5
2
{\displaystyle 4x^{2}+48x+{\frac {5}{2}}={\frac {5}{2}}}
7
x
2
−
161
5
x
+
1933
175
=
−
5
7
{\displaystyle 7x^{2}-{\frac {161}{5}}x+{\frac {1933}{175}}=-{\frac {5}{7}}}
תשובות סופיות
עריכה
{
−
13
2
,
15
2
}
{\displaystyle \left\{-{\frac {13}{2}},{\frac {15}{2}}\right\}}
{
21
5
,
−
20
3
}
{\displaystyle \left\{{\frac {21}{5}},-{\frac {20}{3}}\right\}}
{
17
2
,
−
19
}
{\displaystyle \left\{{\frac {17}{2}},-19\right\}}
{
−
12
,
9
2
}
{\displaystyle \left\{-12,{\frac {9}{2}}\right\}}
{
13
3
,
−
12
7
}
{\displaystyle \left\{{\frac {13}{3}},-{\frac {12}{7}}\right\}}
{
−
3
4
,
−
3
}
{\displaystyle \left\{-{\frac {3}{4}},-3\right\}}
{
18
5
,
−
11
3
}
{\displaystyle \left\{{\frac {18}{5}},-{\frac {11}{3}}\right\}}
{
17
6
,
−
10
3
}
{\displaystyle \left\{{\frac {17}{6}},-{\frac {10}{3}}\right\}}
{
−
12
7
,
−
17
}
{\displaystyle \left\{-{\frac {12}{7}},-17\right\}}
{
3
2
,
11
7
}
{\displaystyle \left\{{\frac {3}{2}},{\frac {11}{7}}\right\}}
{
−
8
5
,
−
1
}
{\displaystyle \left\{-{\frac {8}{5}},-1\right\}}
{
−
1
2
,
−
14
5
}
{\displaystyle \left\{-{\frac {1}{2}},-{\frac {14}{5}}\right\}}
{
14
5
,
17
2
}
{\displaystyle \left\{{\frac {14}{5}},{\frac {17}{2}}\right\}}
{
2
,
11
7
}
{\displaystyle \left\{2,{\frac {11}{7}}\right\}}
{
−
13
2
,
−
18
5
}
{\displaystyle \left\{-{\frac {13}{2}},-{\frac {18}{5}}\right\}}
{
2
3
,
−
6
}
{\displaystyle \left\{{\frac {2}{3}},-6\right\}}
{
−
11
4
,
−
4
}
{\displaystyle \left\{-{\frac {11}{4}},-4\right\}}
{
18
7
,
−
11
3
}
{\displaystyle \left\{{\frac {18}{7}},-{\frac {11}{3}}\right\}}
{
9
2
,
5
4
}
{\displaystyle \left\{{\frac {9}{2}},{\frac {5}{4}}\right\}}
{
−
11
7
,
−
3
}
{\displaystyle \left\{-{\frac {11}{7}},-3\right\}}
{
−
19
,
−
8
}
{\displaystyle \{-19,-8\}}
{
11
5
,
10
3
}
{\displaystyle \left\{{\frac {11}{5}},{\frac {10}{3}}\right\}}
{
−
7
2
,
−
3
2
}
{\displaystyle \left\{-{\frac {7}{2}},-{\frac {3}{2}}\right\}}
{
−
1
,
3
}
{\displaystyle \{-1,3\}}
{
1
7
,
−
4
}
{\displaystyle \left\{{\frac {1}{7}},-4\right\}}
{
0
,
−
6
7
}
{\displaystyle \left\{0,-{\frac {6}{7}}\right\}}
{
13
}
{\displaystyle \{13\}}
{
8
7
,
17
7
}
{\displaystyle \left\{{\frac {8}{7}},{\frac {17}{7}}\right\}}
{
4
5
,
−
3
4
}
{\displaystyle \left\{{\frac {4}{5}},-{\frac {3}{4}}\right\}}
{
21
4
,
−
5
}
{\displaystyle \left\{{\frac {21}{4}},-5\right\}}
{
3
,
4
5
}
{\displaystyle \left\{3,{\frac {4}{5}}\right\}}
{
−
3
4
,
−
8
}
{\displaystyle \left\{-{\frac {3}{4}},-8\right\}}
{
15
7
,
19
3
}
{\displaystyle \left\{{\frac {15}{7}},{\frac {19}{3}}\right\}}
{
1
,
−
2
}
{\displaystyle \{1,-2\}}
{
−
10
,
1
}
{\displaystyle \{-10,1\}}
{
0
,
4
7
}
{\displaystyle \left\{0,{\frac {4}{7}}\right\}}
{
4
3
,
17
}
{\displaystyle \left\{{\frac {4}{3}},17\right\}}
{
13
5
,
−
21
5
}
{\displaystyle \left\{{\frac {13}{5}},-{\frac {21}{5}}\right\}}
{
−
10
,
2
}
{\displaystyle \{-10,2\}}
{
−
19
6
,
−
9
2
}
{\displaystyle \left\{-{\frac {19}{6}},-{\frac {9}{2}}\right\}}
{
1
2
,
−
6
}
{\displaystyle \left\{{\frac {1}{2}},-6\right\}}
{
−
3
7
,
−
11
7
}
{\displaystyle \left\{-{\frac {3}{7}},-{\frac {11}{7}}\right\}}
{
1
,
11
}
{\displaystyle \{1,11\}}
{
9
2
,
−
5
2
}
{\displaystyle \left\{{\frac {9}{2}},-{\frac {5}{2}}\right\}}
{
−
10
3
,
1
2
}
{\displaystyle \left\{-{\frac {10}{3}},{\frac {1}{2}}\right\}}
{
−
21
,
−
9
}
{\displaystyle \{-21,-9\}}
{
−
5
2
,
−
1
}
{\displaystyle \left\{-{\frac {5}{2}},-1\right\}}
{
−
1
2
,
1
7
}
{\displaystyle \left\{-{\frac {1}{2}},{\frac {1}{7}}\right\}}
{
0
,
−
12
}
{\displaystyle \{0,-12\}}
{
21
5
,
2
5
}
{\displaystyle \left\{{\frac {21}{5}},{\frac {2}{5}}\right\}}
