Whakaoti i te (w-1)^2-3^2=0

$$( w - 1 ) ^ { 2 } - 3 ^ { 2 } = 0$$

Whakaoti mō w

$$w=4$$

$$w=-2$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(w-1\right)^{2}.

$$w^{2}-2w+1-3^{2}=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$w^{2}-2w+1-9=0$$

Tangohia te 9 i te 1, ka -8.

$$w^{2}-2w-8=0$$

Hei whakaoti i te whārite, whakatauwehea te w^{2}-2w-8 mā te whakamahi i te tātai w^{2}+\left(a+b\right)w+ab=\left(w+a\right)\left(w+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=-8$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -8.

$$1,-8 2,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-8=-7 2-4=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-4 b=2$$

Me tuhi anō te kīanga whakatauwehe \left(w+a\right)\left(w+b\right) mā ngā uara i tātaihia.

$$\left(w-4\right)\left(w+2\right)$$

Hei kimi otinga whārite, me whakaoti te w-4=0 me te w+2=0.

$$w=4 w=-2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(w-1\right)^{2}.

$$w^{2}-2w+1-3^{2}=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$w^{2}-2w+1-9=0$$

Tangohia te 9 i te 1, ka -8.

$$w^{2}-2w-8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei w^{2}+aw+bw-8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-8\right)=-8$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -8.

$$1,-8 2,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-8=-7 2-4=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-4 b=2$$

Tuhia anō te w^{2}-2w-8 hei \left(w^{2}-4w\right)+\left(2w-8\right).

$$\left(w^{2}-4w\right)+\left(2w-8\right)$$

Tauwehea te w i te tuatahi me te 2 i te rōpū tuarua.

$$w\left(w-4\right)+2\left(w-4\right)$$

Whakatauwehea atu te kīanga pātahi w-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-4\right)\left(w+2\right)$$

Hei kimi otinga whārite, me whakaoti te w-4=0 me te w+2=0.

$$w=4 w=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(w-1\right)^{2}.

$$w^{2}-2w+1-3^{2}=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$w^{2}-2w+1-9=0$$

Tangohia te 9 i te 1, ka -8.

$$w^{2}-2w-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}$$

Pūrua -2.

$$w=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)}}{2}$$

Whakareatia -4 ki te -8.

$$w=\frac{-\left(-2\right)±\sqrt{4+32}}{2}$$

Tāpiri 4 ki te 32.

$$w=\frac{-\left(-2\right)±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$w=\frac{-\left(-2\right)±6}{2}$$

Ko te tauaro o -2 ko 2.

$$w=\frac{2±6}{2}$$

Nā, me whakaoti te whārite w=\frac{2±6}{2} ina he tāpiri te ±. Tāpiri 2 ki te 6.

$$w=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$w=4$$

Nā, me whakaoti te whārite w=\frac{2±6}{2} ina he tango te ±. Tango 6 mai i 2.

$$w=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$w=-2$$

Kua oti te whārite te whakatau.

$$w=4 w=-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(w-1\right)^{2}.

$$w^{2}-2w+1-3^{2}=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$w^{2}-2w+1-9=0$$

Tangohia te 9 i te 1, ka -8.

$$w^{2}-2w-8=0$$

Me tāpiri te 8 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$w^{2}-2w=8$$

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}-2w+1=8+1$$

Tāpiri 8 ki te 1.

$$w^{2}-2w+1=9$$

Tauwehea w^{2}-2w+1. 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}.

$$\left(w-1\right)^{2}=9$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(w-1\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$w-1=3 w-1=-3$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$w=4 w=-2$$