Whakaoti i te 4a^2-9/2a-3=9

$$\frac { 4 a ^ { 2 } - 9 } { 2 a - 3 } = 9$$

Whakaoti mō a

$$a=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe a ki \frac{3}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2a-3.

$$4a^{2}-9=9\left(2a-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te 2a-3.

$$4a^{2}-9=18a-27$$

Tangohia te 18a mai i ngā taha e rua.

$$4a^{2}-9-18a=-27$$

Me tāpiri te 27 ki ngā taha e rua.

$$4a^{2}-9-18a+27=0$$

Tāpirihia te -9 ki te 27, ka 18.

$$4a^{2}+18-18a=0$$

Whakawehea ngā taha e rua ki te 2.

$$2a^{2}+9-9a=0$$

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

$$2a^{2}-9a+9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2a^{2}+aa+ba+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-9 ab=2\times 9=18$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 18.

$$-1,-18 -2,-9 -3,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-18=-19 -2-9=-11 -3-6=-9$$

Ko te otinga te takirua ka hoatu i te tapeke -9.

$$a=-6 b=-3$$

Tuhia anō te 2a^{2}-9a+9 hei \left(2a^{2}-6a\right)+\left(-3a+9\right).

$$\left(2a^{2}-6a\right)+\left(-3a+9\right)$$

Tauwehea te 2a i te tuatahi me te -3 i te rōpū tuarua.

$$2a\left(a-3\right)-3\left(a-3\right)$$

Whakatauwehea atu te kīanga pātahi a-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-3\right)\left(2a-3\right)$$

Hei kimi otinga whārite, me whakaoti te a-3=0 me te 2a-3=0.

$$a=3 a=\frac{3}{2}$$

Tē taea kia ōrite te tāupe a ki \frac{3}{2}.

$$a=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe a ki \frac{3}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2a-3.

$$4a^{2}-9=9\left(2a-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te 2a-3.

$$4a^{2}-9=18a-27$$

Tangohia te 18a mai i ngā taha e rua.

$$4a^{2}-9-18a=-27$$

Me tāpiri te 27 ki ngā taha e rua.

$$4a^{2}-9-18a+27=0$$

Tāpirihia te -9 ki te 27, ka 18.

$$4a^{2}+18-18a=0$$

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.

$$4a^{2}-18a+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -18 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 4\times 18}}{2\times 4}$$

Pūrua -18.

$$a=\frac{-\left(-18\right)±\sqrt{324-4\times 4\times 18}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$a=\frac{-\left(-18\right)±\sqrt{324-16\times 18}}{2\times 4}$$

Whakareatia -16 ki te 18.

$$a=\frac{-\left(-18\right)±\sqrt{324-288}}{2\times 4}$$

Tāpiri 324 ki te -288.

$$a=\frac{-\left(-18\right)±\sqrt{36}}{2\times 4}$$

Tuhia te pūtakerua o te 36.

$$a=\frac{-\left(-18\right)±6}{2\times 4}$$

Ko te tauaro o -18 ko 18.

$$a=\frac{18±6}{2\times 4}$$

Whakareatia 2 ki te 4.

$$a=\frac{18±6}{8}$$

Nā, me whakaoti te whārite a=\frac{18±6}{8} ina he tāpiri te ±. Tāpiri 18 ki te 6.

$$a=\frac{24}{8}$$

Whakawehe 24 ki te 8.

$$a=3$$

Nā, me whakaoti te whārite a=\frac{18±6}{8} ina he tango te ±. Tango 6 mai i 18.

$$a=\frac{12}{8}$$

Whakahekea te hautanga \frac{12}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$a=\frac{3}{2}$$

Kua oti te whārite te whakatau.

$$a=3 a=\frac{3}{2}$$

Tē taea kia ōrite te tāupe a ki \frac{3}{2}.

$$a=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe a ki \frac{3}{2} nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 2a-3.

$$4a^{2}-9=9\left(2a-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te 2a-3.

$$4a^{2}-9=18a-27$$

Tangohia te 18a mai i ngā taha e rua.

$$4a^{2}-9-18a=-27$$

Me tāpiri te 9 ki ngā taha e rua.

$$4a^{2}-18a=-27+9$$

Tāpirihia te -27 ki te 9, ka -18.

$$4a^{2}-18a=-18$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4a^{2}-18a}{4}=-\frac{18}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$a^{2}+\left(-\frac{18}{4}\right)a=-\frac{18}{4}$$

Whakahekea te hautanga \frac{-18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}-\frac{9}{2}a=-\frac{18}{4}$$

Whakahekea te hautanga \frac{-18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$a^{2}-\frac{9}{2}a=-\frac{9}{2}$$

Whakawehea te -\frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{4}. Nā, tāpiria te pūrua o te -\frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-\frac{9}{2}a+\left(-\frac{9}{4}\right)^{2}=-\frac{9}{2}+\left(-\frac{9}{4}\right)^{2}$$

Pūruatia -\frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}-\frac{9}{2}a+\frac{81}{16}=-\frac{9}{2}+\frac{81}{16}$$

Tāpiri -\frac{9}{2} ki te \frac{81}{16} 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.

$$a^{2}-\frac{9}{2}a+\frac{81}{16}=\frac{9}{16}$$

Tauwehea a^{2}-\frac{9}{2}a+\frac{81}{16}. 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}.

$$\left(a-\frac{9}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(a-\frac{9}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$a-\frac{9}{4}=\frac{3}{4} a-\frac{9}{4}=-\frac{3}{4}$$

Me tāpiri \frac{9}{4} ki ngā taha e rua o te whārite.

$$a=3 a=\frac{3}{2}$$

Tē taea kia ōrite te tāupe a ki \frac{3}{2}.

$$a=3$$