Whakaoti i te 9x+7/7x-9=4-0x/4x-7

$$\frac { 9 x + 7 } { 7 x - 9 } = \frac { 4 - 0 x } { 4 x - 7 }$$

Whakaoti mō x

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8}\approx 1.936478267$$

$$x=-\frac{\sqrt{649}}{24}+\frac{7}{8}\approx -0.186478267$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara \frac{9}{7},\frac{7}{4} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(4x-7\right)\left(7x-9\right), arā, te tauraro pātahi he tino iti rawa te kitea o 7x-9,4x-7.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(4-0x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x-7 ki te 9x+7 ka whakakotahi i ngā kupu rite.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0x\right)$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0\right)$$

Tangohia te 0 i te 4, ka 4.

$$36x^{2}-35x-49=\left(7x-9\right)\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7x-9 ki te 4.

$$36x^{2}-35x-49=28x-36$$

Tangohia te 28x mai i ngā taha e rua.

$$36x^{2}-35x-49-28x=-36$$

Pahekotia te -35x me -28x, ka -63x.

$$36x^{2}-63x-49=-36$$

Me tāpiri te 36 ki ngā taha e rua.

$$36x^{2}-63x-49+36=0$$

Tāpirihia te -49 ki te 36, ka -13.

$$36x^{2}-63x-13=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, -63 mō b, me -13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-63\right)±\sqrt{\left(-63\right)^{2}-4\times 36\left(-13\right)}}{2\times 36}$$

Pūrua -63.

$$x=\frac{-\left(-63\right)±\sqrt{3969-4\times 36\left(-13\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-\left(-63\right)±\sqrt{3969-144\left(-13\right)}}{2\times 36}$$

Whakareatia -144 ki te -13.

$$x=\frac{-\left(-63\right)±\sqrt{3969+1872}}{2\times 36}$$

Tāpiri 3969 ki te 1872.

$$x=\frac{-\left(-63\right)±\sqrt{5841}}{2\times 36}$$

Tuhia te pūtakerua o te 5841.

$$x=\frac{-\left(-63\right)±3\sqrt{649}}{2\times 36}$$

Ko te tauaro o -63 ko 63.

$$x=\frac{63±3\sqrt{649}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{63±3\sqrt{649}}{72}$$

Nā, me whakaoti te whārite x=\frac{63±3\sqrt{649}}{72} ina he tāpiri te ±. Tāpiri 63 ki te 3\sqrt{649}.

$$x=\frac{3\sqrt{649}+63}{72}$$

Whakawehe 63+3\sqrt{649} ki te 72.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8}$$

Nā, me whakaoti te whārite x=\frac{63±3\sqrt{649}}{72} ina he tango te ±. Tango 3\sqrt{649} mai i 63.

$$x=\frac{63-3\sqrt{649}}{72}$$

Whakawehe 63-3\sqrt{649} ki te 72.

$$x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8} x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara \frac{9}{7},\frac{7}{4} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(4x-7\right)\left(7x-9\right), arā, te tauraro pātahi he tino iti rawa te kitea o 7x-9,4x-7.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(4-0x\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x-7 ki te 9x+7 ka whakakotahi i ngā kupu rite.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0x\right)$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0\right)$$

Tangohia te 0 i te 4, ka 4.

$$36x^{2}-35x-49=\left(7x-9\right)\times 4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7x-9 ki te 4.

$$36x^{2}-35x-49=28x-36$$

Tangohia te 28x mai i ngā taha e rua.

$$36x^{2}-35x-49-28x=-36$$

Pahekotia te -35x me -28x, ka -63x.

$$36x^{2}-63x-49=-36$$

Me tāpiri te 49 ki ngā taha e rua.

$$36x^{2}-63x=-36+49$$

Tāpirihia te -36 ki te 49, ka 13.

$$36x^{2}-63x=13$$

Whakawehea ngā taha e rua ki te 36.

$$\frac{36x^{2}-63x}{36}=\frac{13}{36}$$

Mā te whakawehe ki te 36 ka wetekia te whakareanga ki te 36.

$$x^{2}+\left(-\frac{63}{36}\right)x=\frac{13}{36}$$

Whakahekea te hautanga \frac{-63}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$x^{2}-\frac{7}{4}x=\frac{13}{36}$$

Whakawehea te -\frac{7}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{8}. Nā, tāpiria te pūrua o te -\frac{7}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7}{4}x+\left(-\frac{7}{8}\right)^{2}=\frac{13}{36}+\left(-\frac{7}{8}\right)^{2}$$

Pūruatia -\frac{7}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{4}x+\frac{49}{64}=\frac{13}{36}+\frac{49}{64}$$

Tāpiri \frac{13}{36} ki te \frac{49}{64} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{7}{4}x+\frac{49}{64}=\frac{649}{576}$$

Tauwehea x^{2}-\frac{7}{4}x+\frac{49}{64}. 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}.

$$\left(x-\frac{7}{8}\right)^{2}=\frac{649}{576}$$

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

$$\sqrt{\left(x-\frac{7}{8}\right)^{2}}=\sqrt{\frac{649}{576}}$$

Whakarūnātia.

$$x-\frac{7}{8}=\frac{\sqrt{649}}{24} x-\frac{7}{8}=-\frac{\sqrt{649}}{24}$$

Me tāpiri \frac{7}{8} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8} x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$