Whakaoti i te 34-y=120/y

$$34 - y = \frac { 120 } { y }$$

Whakaoti mō y

$$y=4$$

$$y=30$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$y\times 34-yy=120$$

Whakareatia te y ki te y, ka y^{2}.

$$y\times 34-y^{2}=120$$

Tangohia te 120 mai i ngā taha e rua.

$$y\times 34-y^{2}-120=0$$

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.

$$-y^{2}+34y-120=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 34 mō b, me -120 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-34±\sqrt{34^{2}-4\left(-1\right)\left(-120\right)}}{2\left(-1\right)}$$

Pūrua 34.

$$y=\frac{-34±\sqrt{1156-4\left(-1\right)\left(-120\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$y=\frac{-34±\sqrt{1156+4\left(-120\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -120.

$$y=\frac{-34±\sqrt{1156-480}}{2\left(-1\right)}$$

Tāpiri 1156 ki te -480.

$$y=\frac{-34±\sqrt{676}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 676.

$$y=\frac{-34±26}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$y=\frac{-34±26}{-2}$$

Nā, me whakaoti te whārite y=\frac{-34±26}{-2} ina he tāpiri te ±. Tāpiri -34 ki te 26.

$$y=-\frac{8}{-2}$$

Whakawehe -8 ki te -2.

$$y=4$$

Nā, me whakaoti te whārite y=\frac{-34±26}{-2} ina he tango te ±. Tango 26 mai i -34.

$$y=-\frac{60}{-2}$$

Whakawehe -60 ki te -2.

$$y=30$$

Kua oti te whārite te whakatau.

$$y=4 y=30$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$y\times 34-yy=120$$

Whakareatia te y ki te y, ka y^{2}.

$$y\times 34-y^{2}=120$$

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.

$$-y^{2}+34y=120$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y^{2}+34y}{-1}=\frac{120}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$y^{2}+\frac{34}{-1}y=\frac{120}{-1}$$

Whakawehe 34 ki te -1.

$$y^{2}-34y=\frac{120}{-1}$$

Whakawehe 120 ki te -1.

$$y^{2}-34y=-120$$

Whakawehea te -34, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -17. Nā, tāpiria te pūrua o te -17 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-34y+\left(-17\right)^{2}=-120+\left(-17\right)^{2}$$

Pūrua -17.

$$y^{2}-34y+289=-120+289$$

Tāpiri -120 ki te 289.

$$y^{2}-34y+289=169$$

Tauwehea y^{2}-34y+289. 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}.

$$\left(y-17\right)^{2}=169$$

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

$$\sqrt{\left(y-17\right)^{2}}=\sqrt{169}$$

Whakarūnātia.

$$y-17=13 y-17=-13$$

Me tāpiri 17 ki ngā taha e rua o te whārite.

$$y=30 y=4$$