Whakaoti mō x
x=\frac{1}{3}\approx 0.333333333
x=2
Graph
Tohaina
Kua tāruatia ki te papatopenga
a+b=-7 ab=3\times 2=6
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 3x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-6 -2,-3
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 6.
-1-6=-7 -2-3=-5
Tātaihia te tapeke mō ia takirua.
a=-6 b=-1
Ko te otinga te takirua ka hoatu i te tapeke -7.
\left(3x^{2}-6x\right)+\left(-x+2\right)
Tuhia anō te 3x^{2}-7x+2 hei \left(3x^{2}-6x\right)+\left(-x+2\right).
3x\left(x-2\right)-\left(x-2\right)
Tauwehea te 3x i te tuatahi me te -1 i te rōpū tuarua.
\left(x-2\right)\left(3x-1\right)
Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
x=2 x=\frac{1}{3}
Hei kimi otinga whārite, me whakaoti te x-2=0 me te 3x-1=0.
3x^{2}-7x+2=0
Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.
x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 3\times 2}}{2\times 3}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -7 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-7\right)±\sqrt{49-4\times 3\times 2}}{2\times 3}
Pūrua -7.
x=\frac{-\left(-7\right)±\sqrt{49-12\times 2}}{2\times 3}
Whakareatia -4 ki te 3.
x=\frac{-\left(-7\right)±\sqrt{49-24}}{2\times 3}
Whakareatia -12 ki te 2.
x=\frac{-\left(-7\right)±\sqrt{25}}{2\times 3}
Tāpiri 49 ki te -24.
x=\frac{-\left(-7\right)±5}{2\times 3}
Tuhia te pūtakerua o te 25.
x=\frac{7±5}{2\times 3}
Ko te tauaro o -7 ko 7.
x=\frac{7±5}{6}
Whakareatia 2 ki te 3.
x=\frac{12}{6}
Nā, me whakaoti te whārite x=\frac{7±5}{6} ina he tāpiri te ±. Tāpiri 7 ki te 5.
x=2
Whakawehe 12 ki te 6.
x=\frac{2}{6}
Nā, me whakaoti te whārite x=\frac{7±5}{6} ina he tango te ±. Tango 5 mai i 7.
x=\frac{1}{3}
Whakahekea te hautanga \frac{2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x=2 x=\frac{1}{3}
Kua oti te whārite te whakatau.
3x^{2}-7x+2=0
Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.
3x^{2}-7x+2-2=-2
Me tango 2 mai i ngā taha e rua o te whārite.
3x^{2}-7x=-2
Mā te tango i te 2 i a ia ake anō ka toe ko te 0.
\frac{3x^{2}-7x}{3}=-\frac{2}{3}
Whakawehea ngā taha e rua ki te 3.
x^{2}-\frac{7}{3}x=-\frac{2}{3}
Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.
x^{2}-\frac{7}{3}x+\left(-\frac{7}{6}\right)^{2}=-\frac{2}{3}+\left(-\frac{7}{6}\right)^{2}
Whakawehea te -\frac{7}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{6}. Nā, tāpiria te pūrua o te -\frac{7}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{7}{3}x+\frac{49}{36}=-\frac{2}{3}+\frac{49}{36}
Pūruatia -\frac{7}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{7}{3}x+\frac{49}{36}=\frac{25}{36}
Tāpiri -\frac{2}{3} ki te \frac{49}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
\left(x-\frac{7}{6}\right)^{2}=\frac{25}{36}
Tauwehea te x^{2}-\frac{7}{3}x+\frac{49}{36}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{7}{6}\right)^{2}}=\sqrt{\frac{25}{36}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{7}{6}=\frac{5}{6} x-\frac{7}{6}=-\frac{5}{6}
Whakarūnātia.
x=2 x=\frac{1}{3}
Me tāpiri \frac{7}{6} ki ngā taha e rua o te whārite.
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