Whakaoti i te (2008-x)(2006-x)=2007

$$(2008-x)(2006-x)=2007$$

Whakaoti mō x

$$x=2007-2\sqrt{502}\approx 1962.189286995$$

$$x=2\sqrt{502}+2007\approx 2051.810713005$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2008-x ki te 2006-x ka whakakotahi i ngā kupu rite.

$$4028048-4014x+x^{2}=2007$$

Tangohia te 2007 mai i ngā taha e rua.

$$4028048-4014x+x^{2}-2007=0$$

Tangohia te 2007 i te 4028048, ka 4026041.

$$4026041-4014x+x^{2}=0$$

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.

$$x^{2}-4014x+4026041=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4014 mō b, me 4026041 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4014\right)±\sqrt{\left(-4014\right)^{2}-4\times 4026041}}{2}$$

Pūrua -4014.

$$x=\frac{-\left(-4014\right)±\sqrt{16112196-4\times 4026041}}{2}$$

Whakareatia -4 ki te 4026041.

$$x=\frac{-\left(-4014\right)±\sqrt{16112196-16104164}}{2}$$

Tāpiri 16112196 ki te -16104164.

$$x=\frac{-\left(-4014\right)±\sqrt{8032}}{2}$$

Tuhia te pūtakerua o te 8032.

$$x=\frac{-\left(-4014\right)±4\sqrt{502}}{2}$$

Ko te tauaro o -4014 ko 4014.

$$x=\frac{4014±4\sqrt{502}}{2}$$

Nā, me whakaoti te whārite x=\frac{4014±4\sqrt{502}}{2} ina he tāpiri te ±. Tāpiri 4014 ki te 4\sqrt{502}.

$$x=\frac{4\sqrt{502}+4014}{2}$$

Whakawehe 4014+4\sqrt{502} ki te 2.

$$x=2\sqrt{502}+2007$$

Nā, me whakaoti te whārite x=\frac{4014±4\sqrt{502}}{2} ina he tango te ±. Tango 4\sqrt{502} mai i 4014.

$$x=\frac{4014-4\sqrt{502}}{2}$$

Whakawehe 4014-4\sqrt{502} ki te 2.

$$x=2007-2\sqrt{502}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{502}+2007 x=2007-2\sqrt{502}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2008-x ki te 2006-x ka whakakotahi i ngā kupu rite.

$$4028048-4014x+x^{2}=2007$$

Tangohia te 4028048 mai i ngā taha e rua.

$$-4014x+x^{2}=2007-4028048$$

Tangohia te 4028048 i te 2007, ka -4026041.

$$-4014x+x^{2}=-4026041$$

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.

$$x^{2}-4014x=-4026041$$

Whakawehea te -4014, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2007. Nā, tāpiria te pūrua o te -2007 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-4014x+\left(-2007\right)^{2}=-4026041+\left(-2007\right)^{2}$$

Pūrua -2007.

$$x^{2}-4014x+4028049=-4026041+4028049$$

Tāpiri -4026041 ki te 4028049.

$$x^{2}-4014x+4028049=2008$$

Tauwehea x^{2}-4014x+4028049. 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}.

$$\left(x-2007\right)^{2}=2008$$

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

$$\sqrt{\left(x-2007\right)^{2}}=\sqrt{2008}$$

Whakarūnātia.

$$x-2007=2\sqrt{502} x-2007=-2\sqrt{502}$$

Me tāpiri 2007 ki ngā taha e rua o te whārite.

$$x=2\sqrt{502}+2007 x=2007-2\sqrt{502}$$