Tīpoka ki ngā ihirangi matua
Whakaoti mō x
Tick mark Image
Graph

Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

a+b=-3 ab=2
Hei whakaoti i te whārite, whakatauwehea te x^{2}-3x+2 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-2 b=-1
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x-2\right)\left(x-1\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=2 x=1
Hei kimi otinga whārite, me whakaoti te x-2=0 me te x-1=0.
a+b=-3 ab=1\times 2=2
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-2 b=-1
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}-2x\right)+\left(-x+2\right)
Tuhia anō te x^{2}-3x+2 hei \left(x^{2}-2x\right)+\left(-x+2\right).
x\left(x-2\right)-\left(x-2\right)
Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.
\left(x-2\right)\left(x-1\right)
Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
x=2 x=1
Hei kimi otinga whārite, me whakaoti te x-2=0 me te x-1=0.
x^{2}-3x+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(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-3\right)±\sqrt{9-4\times 2}}{2}
Pūrua -3.
x=\frac{-\left(-3\right)±\sqrt{9-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{-\left(-3\right)±\sqrt{1}}{2}
Tāpiri 9 ki te -8.
x=\frac{-\left(-3\right)±1}{2}
Tuhia te pūtakerua o te 1.
x=\frac{3±1}{2}
Ko te tauaro o -3 ko 3.
x=\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{3±1}{2} ina he tāpiri te ±. Tāpiri 3 ki te 1.
x=2
Whakawehe 4 ki te 2.
x=\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{3±1}{2} ina he tango te ±. Tango 1 mai i 3.
x=1
Whakawehe 2 ki te 2.
x=2 x=1
Kua oti te whārite te whakatau.
x^{2}-3x+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.
x^{2}-3x+2-2=-2
Me tango 2 mai i ngā taha e rua o te whārite.
x^{2}-3x=-2
Mā te tango i te 2 i a ia ake anō ka toe ko te 0.
x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=-2+\left(-\frac{3}{2}\right)^{2}
Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-3x+\frac{9}{4}=-2+\frac{9}{4}
Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-3x+\frac{9}{4}=\frac{1}{4}
Tāpiri -2 ki te \frac{9}{4}.
\left(x-\frac{3}{2}\right)^{2}=\frac{1}{4}
Tauwehea te x^{2}-3x+\frac{9}{4}. 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{3}{2}\right)^{2}}=\sqrt{\frac{1}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{3}{2}=\frac{1}{2} x-\frac{3}{2}=-\frac{1}{2}
Whakarūnātia.
x=2 x=1
Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.