Whakaoti i te 7*8/x+8*7x=x

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

Whakaoti mō x (complex solution)

$$x=-\frac{2\sqrt{770}i}{55}\approx -0-1.009049958i$$

$$x=\frac{2\sqrt{770}i}{55}\approx 1.009049958i$$

Ngā Upane mā te Kimi Pūtakerua

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.

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

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

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

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

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

Whakareatia te 7 ki te 8, ka 56. Whakareatia te 8 ki te 7, ka 56.

$$56+56x^{2}=x^{2}$$

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

$$56+56x^{2}-x^{2}=0$$

Pahekotia te 56x^{2} me -x^{2}, ka 55x^{2}.

$$56+55x^{2}=0$$

Tangohia te 56 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$55x^{2}=-56$$

Whakawehea ngā taha e rua ki te 55.

$$x^{2}=-\frac{56}{55}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{770}i}{55} x=-\frac{2\sqrt{770}i}{55}$$

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.

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

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

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

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

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

Whakareatia te 7 ki te 8, ka 56. Whakareatia te 8 ki te 7, ka 56.

$$56+56x^{2}=x^{2}$$

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

$$56+56x^{2}-x^{2}=0$$

Pahekotia te 56x^{2} me -x^{2}, ka 55x^{2}.

$$56+55x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$55x^{2}+56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 55 mō a, 0 mō b, me 56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 55\times 56}}{2\times 55}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 55\times 56}}{2\times 55}$$

Whakareatia -4 ki te 55.

$$x=\frac{0±\sqrt{-220\times 56}}{2\times 55}$$

Whakareatia -220 ki te 56.

$$x=\frac{0±\sqrt{-12320}}{2\times 55}$$

Tuhia te pūtakerua o te -12320.

$$x=\frac{0±4\sqrt{770}i}{2\times 55}$$

Whakareatia 2 ki te 55.

$$x=\frac{0±4\sqrt{770}i}{110}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{770}i}{110} ina he tāpiri te ±.

$$x=\frac{2\sqrt{770}i}{55}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{770}i}{110} ina he tango te ±.

$$x=-\frac{2\sqrt{770}i}{55}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{770}i}{55} x=-\frac{2\sqrt{770}i}{55}$$