Whakaoti i te 7+8/x=x

$$7 + \frac { 8 } { x } = x$$

Whakaoti mō x

$$x=-1$$

$$x=8$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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.

$$x\times 7+8=xx$$

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

$$x\times 7+8=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x\times 7+8-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+7x+8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=7 ab=-8=-8$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -8.

$$-1,8 -2,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+8=7 -2+4=2$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$a=8 b=-1$$

Tuhia anō te -x^{2}+7x+8 hei \left(-x^{2}+8x\right)+\left(-x+8\right).

$$\left(-x^{2}+8x\right)+\left(-x+8\right)$$

Tauwehea te -x i te tuatahi me te -1 i te rōpū tuarua.

$$-x\left(x-8\right)-\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(-x-1\right)$$

Hei kimi otinga whārite, me whakaoti te x-8=0 me te -x-1=0.

$$x=8 x=-1$$

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.

$$x\times 7+8=xx$$

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

$$x\times 7+8=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x\times 7+8-x^{2}=0$$

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.

$$-x^{2}+7x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 7 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-7±\sqrt{49+4\times 8}}{2\left(-1\right)}$$

Whakareatia 4 ki te 8.

$$x=\frac{-7±\sqrt{49+32}}{2\left(-1\right)}$$

Tāpiri 49 ki te 32.

$$x=\frac{-7±\sqrt{81}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-7±9}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-7±9}{-2}$$

Nā, me whakaoti te whārite x=\frac{-7±9}{-2} ina he tāpiri te ±. Tāpiri -7 ki te 9.

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

Whakawehe 2 ki te -2.

$$x=-1$$

Nā, me whakaoti te whārite x=\frac{-7±9}{-2} ina he tango te ±. Tango 9 mai i -7.

$$x=-\frac{16}{-2}$$

Whakawehe -16 ki te -2.

$$x=8$$

Kua oti te whārite te whakatau.

$$x=-1 x=8$$

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.

$$x\times 7+8=xx$$

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

$$x\times 7+8=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$x\times 7+8-x^{2}=0$$

Tangohia te 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x\times 7-x^{2}=-8$$

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.

$$-x^{2}+7x=-8$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+7x}{-1}=-\frac{8}{-1}$$

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

$$x^{2}+\frac{7}{-1}x=-\frac{8}{-1}$$

Whakawehe 7 ki te -1.

$$x^{2}-7x=-\frac{8}{-1}$$

Whakawehe -8 ki te -1.

$$x^{2}-7x=8$$

Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=8+\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-7x+\frac{49}{4}=8+\frac{49}{4}$$

Tāpiri 8 ki te \frac{49}{4}.

$$x^{2}-7x+\frac{49}{4}=\frac{81}{4}$$

Tauwehea x^{2}-7x+\frac{49}{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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{9}{2} x-\frac{7}{2}=-\frac{9}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=8 x=-1$$