Whakaoti i te 45-x=5/x

$$45 - x = \frac { 5 } { x }$$

Whakaoti mō x

$$x = \frac{\sqrt{2005} + 45}{2} \approx 44.888613177$$

$$x=\frac{45-\sqrt{2005}}{2}\approx 0.111386823$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$x\times 45-xx=5$$

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

$$x\times 45-x^{2}=5$$

Tangohia te 5 mai i ngā taha e rua.

$$x\times 45-x^{2}-5=0$$

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.

$$-x^{2}+45x-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 45 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-45±\sqrt{45^{2}-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}$$

Pūrua 45.

$$x=\frac{-45±\sqrt{2025-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-45±\sqrt{2025+4\left(-5\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -5.

$$x=\frac{-45±\sqrt{2025-20}}{2\left(-1\right)}$$

Tāpiri 2025 ki te -20.

$$x=\frac{-45±\sqrt{2005}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-45±\sqrt{2005}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-45±\sqrt{2005}}{-2} ina he tāpiri te ±. Tāpiri -45 ki te \sqrt{2005}.

$$x=\frac{\sqrt{2005}-45}{-2}$$

Whakawehe -45+\sqrt{2005} ki te -2.

$$x=\frac{45-\sqrt{2005}}{2}$$

Nā, me whakaoti te whārite x=\frac{-45±\sqrt{2005}}{-2} ina he tango te ±. Tango \sqrt{2005} mai i -45.

$$x=\frac{-\sqrt{2005}-45}{-2}$$

Whakawehe -45-\sqrt{2005} ki te -2.

$$x=\frac{\sqrt{2005}+45}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{45-\sqrt{2005}}{2} x=\frac{\sqrt{2005}+45}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$x\times 45-xx=5$$

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

$$x\times 45-x^{2}=5$$

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.

$$-x^{2}+45x=5$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+45x}{-1}=\frac{5}{-1}$$

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

$$x^{2}+\frac{45}{-1}x=\frac{5}{-1}$$

Whakawehe 45 ki te -1.

$$x^{2}-45x=\frac{5}{-1}$$

Whakawehe 5 ki te -1.

$$x^{2}-45x=-5$$

Whakawehea te -45, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{45}{2}. Nā, tāpiria te pūrua o te -\frac{45}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-45x+\left(-\frac{45}{2}\right)^{2}=-5+\left(-\frac{45}{2}\right)^{2}$$

Pūruatia -\frac{45}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-45x+\frac{2025}{4}=-5+\frac{2025}{4}$$

Tāpiri -5 ki te \frac{2025}{4}.

$$x^{2}-45x+\frac{2025}{4}=\frac{2005}{4}$$

Tauwehea x^{2}-45x+\frac{2025}{4}. 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}.

$$\left(x-\frac{45}{2}\right)^{2}=\frac{2005}{4}$$

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

$$\sqrt{\left(x-\frac{45}{2}\right)^{2}}=\sqrt{\frac{2005}{4}}$$

Whakarūnātia.

$$x-\frac{45}{2}=\frac{\sqrt{2005}}{2} x-\frac{45}{2}=-\frac{\sqrt{2005}}{2}$$

Me tāpiri \frac{45}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{2005}+45}{2} x=\frac{45-\sqrt{2005}}{2}$$