Whakaoti i te 17=1+(x-1)*(x-1)

$$17=1+(x-1) \times (x-1)$$

Whakaoti mō x

$$x=5$$

$$x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x-1 ki te x-1, ka \left(x-1\right)^{2}.

$$17=1+\left(x-1\right)^{2}$$

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

$$17=1+x^{2}-2x+1$$

Tāpirihia te 1 ki te 1, ka 2.

$$17=2+x^{2}-2x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2+x^{2}-2x=17$$

Tangohia te 17 mai i ngā taha e rua.

$$2+x^{2}-2x-17=0$$

Tangohia te 17 i te 2, ka -15.

$$-15+x^{2}-2x=0$$

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.

$$x^{2}-2x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-15\right)}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-\left(-2\right)±\sqrt{4+60}}{2}$$

Tāpiri 4 ki te 60.

$$x=\frac{-\left(-2\right)±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-\left(-2\right)±8}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±8}{2}$$

Nā, me whakaoti te whārite x=\frac{2±8}{2} ina he tāpiri te ±. Tāpiri 2 ki te 8.

$$x=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{2±8}{2} ina he tango te ±. Tango 8 mai i 2.

$$x=-\frac{6}{2}$$

Whakawehe -6 ki te 2.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=5 x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x-1 ki te x-1, ka \left(x-1\right)^{2}.

$$17=1+\left(x-1\right)^{2}$$

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

$$17=1+x^{2}-2x+1$$

Tāpirihia te 1 ki te 1, ka 2.

$$17=2+x^{2}-2x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$2+x^{2}-2x=17$$

Tangohia te 2 mai i ngā taha e rua.

$$x^{2}-2x=17-2$$

Tangohia te 2 i te 17, ka 15.

$$x^{2}-2x=15$$

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.

$$x^{2}-2x+1=15+1$$

Tāpiri 15 ki te 1.

$$x^{2}-2x+1=16$$

Tauwehea te x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=16$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x-1=4 x-1=-4$$

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

$$x=5 x=-3$$