Whakaoti i te 6x^2-13x+4=4-2

$$6 x ^ { 2 } - 13 x + 4 = 4 - 2$$

Whakaoti mō x

$$x=\frac{1}{6}\approx 0.166666667$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 2 i te 4, ka 2.

$$6x^{2}-13x+4=2$$

Tangohia te 2 mai i ngā taha e rua.

$$6x^{2}-13x+4-2=0$$

Tangohia te 2 i te 4, ka 2.

$$6x^{2}-13x+2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=6\times 2=12$$

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 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-12 b=-1$$

Tuhia anō te 6x^{2}-13x+2 hei \left(6x^{2}-12x\right)+\left(-x+2\right).

$$\left(6x^{2}-12x\right)+\left(-x+2\right)$$

Tauwehea te 6x i te tuatahi me te -1 i te rōpū tuarua.

$$6x\left(x-2\right)-\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(6x-1\right)$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te 6x-1=0.

$$x=2 x=\frac{1}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2 i te 4, ka 2.

$$6x^{2}-13x+4=2$$

Tangohia te 2 mai i ngā taha e rua.

$$6x^{2}-13x+4-2=0$$

Tangohia te 2 i te 4, ka 2.

$$6x^{2}-13x+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -13 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 6\times 2}}{2\times 6}$$

Pūrua -13.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 6\times 2}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-13\right)±\sqrt{169-24\times 2}}{2\times 6}$$

Whakareatia -24 ki te 2.

$$x=\frac{-\left(-13\right)±\sqrt{169-48}}{2\times 6}$$

Tāpiri 169 ki te -48.

$$x=\frac{-\left(-13\right)±\sqrt{121}}{2\times 6}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-\left(-13\right)±11}{2\times 6}$$

Ko te tauaro o -13 ko 13.

$$x=\frac{13±11}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{13±11}{12}$$

Nā, me whakaoti te whārite x=\frac{13±11}{12} ina he tāpiri te ±. Tāpiri 13 ki te 11.

$$x=\frac{24}{12}$$

Whakawehe 24 ki te 12.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{13±11}{12} ina he tango te ±. Tango 11 mai i 13.

$$x=\frac{2}{12}$$

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{6}$$

Kua oti te whārite te whakatau.

$$x=2 x=\frac{1}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2 i te 4, ka 2.

$$6x^{2}-13x+4=2$$

Tangohia te 4 mai i ngā taha e rua.

$$6x^{2}-13x=2-4$$

Tangohia te 4 i te 2, ka -2.

$$6x^{2}-13x=-2$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-13x}{6}=-\frac{2}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}-\frac{13}{6}x=-\frac{2}{6}$$

Whakahekea te hautanga \frac{-2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{13}{6}x=-\frac{1}{3}$$

Whakawehea te -\frac{13}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{12}. Nā, tāpiria te pūrua o te -\frac{13}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{13}{6}x+\left(-\frac{13}{12}\right)^{2}=-\frac{1}{3}+\left(-\frac{13}{12}\right)^{2}$$

Pūruatia -\frac{13}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=-\frac{1}{3}+\frac{169}{144}$$

Tāpiri -\frac{1}{3} ki te \frac{169}{144} 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.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=\frac{121}{144}$$

Tauwehea x^{2}-\frac{13}{6}x+\frac{169}{144}. 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}.

$$\left(x-\frac{13}{12}\right)^{2}=\frac{121}{144}$$

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

$$\sqrt{\left(x-\frac{13}{12}\right)^{2}}=\sqrt{\frac{121}{144}}$$

Whakarūnātia.

$$x-\frac{13}{12}=\frac{11}{12} x-\frac{13}{12}=-\frac{11}{12}$$

Me tāpiri \frac{13}{12} ki ngā taha e rua o te whārite.

$$x=2 x=\frac{1}{6}$$