Whakaoti i te (2016-x)(2018-x)=2017

$$(2016-x)(2018-x)=2017$$

Whakaoti mō x

$$x=2017-\sqrt{2018}\approx 1972.07784511$$

$$x=\sqrt{2018}+2017\approx 2061.92215489$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2016-x ki te 2018-x ka whakakotahi i ngā kupu rite.

$$4068288-4034x+x^{2}=2017$$

Tangohia te 2017 mai i ngā taha e rua.

$$4068288-4034x+x^{2}-2017=0$$

Tangohia te 2017 i te 4068288, ka 4066271.

$$4066271-4034x+x^{2}=0$$

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.

$$x^{2}-4034x+4066271=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4034 mō b, me 4066271 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4034\right)±\sqrt{\left(-4034\right)^{2}-4\times 4066271}}{2}$$

Pūrua -4034.

$$x=\frac{-\left(-4034\right)±\sqrt{16273156-4\times 4066271}}{2}$$

Whakareatia -4 ki te 4066271.

$$x=\frac{-\left(-4034\right)±\sqrt{16273156-16265084}}{2}$$

Tāpiri 16273156 ki te -16265084.

$$x=\frac{-\left(-4034\right)±\sqrt{8072}}{2}$$

Tuhia te pūtakerua o te 8072.

$$x=\frac{-\left(-4034\right)±2\sqrt{2018}}{2}$$

Ko te tauaro o -4034 ko 4034.

$$x=\frac{4034±2\sqrt{2018}}{2}$$

Nā, me whakaoti te whārite x=\frac{4034±2\sqrt{2018}}{2} ina he tāpiri te ±. Tāpiri 4034 ki te 2\sqrt{2018}.

$$x=\frac{2\sqrt{2018}+4034}{2}$$

Whakawehe 4034+2\sqrt{2018} ki te 2.

$$x=\sqrt{2018}+2017$$

Nā, me whakaoti te whārite x=\frac{4034±2\sqrt{2018}}{2} ina he tango te ±. Tango 2\sqrt{2018} mai i 4034.

$$x=\frac{4034-2\sqrt{2018}}{2}$$

Whakawehe 4034-2\sqrt{2018} ki te 2.

$$x=2017-\sqrt{2018}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{2018}+2017 x=2017-\sqrt{2018}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2016-x ki te 2018-x ka whakakotahi i ngā kupu rite.

$$4068288-4034x+x^{2}=2017$$

Tangohia te 4068288 mai i ngā taha e rua.

$$-4034x+x^{2}=2017-4068288$$

Tangohia te 4068288 i te 2017, ka -4066271.

$$-4034x+x^{2}=-4066271$$

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.

$$x^{2}-4034x=-4066271$$

Whakawehea te -4034, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2017. Nā, tāpiria te pūrua o te -2017 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-4034x+\left(-2017\right)^{2}=-4066271+\left(-2017\right)^{2}$$

Pūrua -2017.

$$x^{2}-4034x+4068289=-4066271+4068289$$

Tāpiri -4066271 ki te 4068289.

$$x^{2}-4034x+4068289=2018$$

Tauwehea x^{2}-4034x+4068289. 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}.

$$\left(x-2017\right)^{2}=2018$$

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

$$\sqrt{\left(x-2017\right)^{2}}=\sqrt{2018}$$

Whakarūnātia.

$$x-2017=\sqrt{2018} x-2017=-\sqrt{2018}$$

Me tāpiri 2017 ki ngā taha e rua o te whārite.

$$x=\sqrt{2018}+2017 x=2017-\sqrt{2018}$$