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a+b=-7 ab=10
Hei whakaoti i te whārite, whakatauwehea te x^{2}-7x+10 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.
-1,-10 -2,-5
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 10.
-1-10=-11 -2-5=-7
Tātaihia te tapeke mō ia takirua.
a=-5 b=-2
Ko te otinga te takirua ka hoatu i te tapeke -7.
\left(x-5\right)\left(x-2\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=5 x=2
Hei kimi otinga whārite, me whakaoti te x-5=0 me te x-2=0.
a+b=-7 ab=1\times 10=10
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-10 -2,-5
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 10.
-1-10=-11 -2-5=-7
Tātaihia te tapeke mō ia takirua.
a=-5 b=-2
Ko te otinga te takirua ka hoatu i te tapeke -7.
\left(x^{2}-5x\right)+\left(-2x+10\right)
Tuhia anō te x^{2}-7x+10 hei \left(x^{2}-5x\right)+\left(-2x+10\right).
x\left(x-5\right)-2\left(x-5\right)
Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.
\left(x-5\right)\left(x-2\right)
Whakatauwehea atu te kīanga pātahi x-5 mā te whakamahi i te āhuatanga tātai tohatoha.
x=5 x=2
Hei kimi otinga whārite, me whakaoti te x-5=0 me te x-2=0.
x^{2}-7x+10=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 10}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -7 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-7\right)±\sqrt{49-4\times 10}}{2}
Pūrua -7.
x=\frac{-\left(-7\right)±\sqrt{49-40}}{2}
Whakareatia -4 ki te 10.
x=\frac{-\left(-7\right)±\sqrt{9}}{2}
Tāpiri 49 ki te -40.
x=\frac{-\left(-7\right)±3}{2}
Tuhia te pūtakerua o te 9.
x=\frac{7±3}{2}
Ko te tauaro o -7 ko 7.
x=\frac{10}{2}
Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tāpiri te ±. Tāpiri 7 ki te 3.
x=5
Whakawehe 10 ki te 2.
x=\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tango te ±. Tango 3 mai i 7.
x=2
Whakawehe 4 ki te 2.
x=5 x=2
Kua oti te whārite te whakatau.
x^{2}-7x+10=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}-7x+10-10=-10
Me tango 10 mai i ngā taha e rua o te whārite.
x^{2}-7x=-10
Mā te tango i te 10 i a ia ake anō ka toe ko te 0.
x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-10+\left(-\frac{7}{2}\right)^{2}
Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-7x+\frac{49}{4}=-10+\frac{49}{4}
Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-7x+\frac{49}{4}=\frac{9}{4}
Tāpiri -10 ki te \frac{49}{4}.
\left(x-\frac{7}{2}\right)^{2}=\frac{9}{4}
Tauwehea x^{2}-7x+\frac{49}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{7}{2}=\frac{3}{2} x-\frac{7}{2}=-\frac{3}{2}
Whakarūnātia.
x=5 x=2
Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.