Whakaoti i te 2(m-6)(m-4)/(m-2)^2=6

$$\frac { 2 ( m - 6 ) ( m - 4 ) } { ( m - 2 ) ^ { 2 } } = 6$$

Whakaoti mō m

$$m=-2$$

$$m=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe m ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(m-2\right)^{2}.

$$2\left(m-6\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te m-6.

$$\left(2m-12\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2m-12 ki te m-4 ka whakakotahi i ngā kupu rite.

$$2m^{2}-20m+48=6\left(m-2\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(m-2\right)^{2}.

$$2m^{2}-20m+48=6\left(m^{2}-4m+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te m^{2}-4m+4.

$$2m^{2}-20m+48=6m^{2}-24m+24$$

Tangohia te 6m^{2} mai i ngā taha e rua.

$$2m^{2}-20m+48-6m^{2}=-24m+24$$

Pahekotia te 2m^{2} me -6m^{2}, ka -4m^{2}.

$$-4m^{2}-20m+48=-24m+24$$

Me tāpiri te 24m ki ngā taha e rua.

$$-4m^{2}-20m+48+24m=24$$

Pahekotia te -20m me 24m, ka 4m.

$$-4m^{2}+4m+48=24$$

Tangohia te 24 mai i ngā taha e rua.

$$-4m^{2}+4m+48-24=0$$

Tangohia te 24 i te 48, ka 24.

$$-4m^{2}+4m+24=0$$

Whakawehea ngā taha e rua ki te 4.

$$-m^{2}+m+6=0$$

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

$$a+b=1 ab=-6=-6$$

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 -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=3 b=-2$$

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

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

Tauwehea te -m i te tuatahi me te -2 i te rōpū tuarua.

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

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

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

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

$$m=3 m=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe m ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(m-2\right)^{2}.

$$2\left(m-6\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te m-6.

$$\left(2m-12\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2m-12 ki te m-4 ka whakakotahi i ngā kupu rite.

$$2m^{2}-20m+48=6\left(m-2\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(m-2\right)^{2}.

$$2m^{2}-20m+48=6\left(m^{2}-4m+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te m^{2}-4m+4.

$$2m^{2}-20m+48=6m^{2}-24m+24$$

Tangohia te 6m^{2} mai i ngā taha e rua.

$$2m^{2}-20m+48-6m^{2}=-24m+24$$

Pahekotia te 2m^{2} me -6m^{2}, ka -4m^{2}.

$$-4m^{2}-20m+48=-24m+24$$

Me tāpiri te 24m ki ngā taha e rua.

$$-4m^{2}-20m+48+24m=24$$

Pahekotia te -20m me 24m, ka 4m.

$$-4m^{2}+4m+48=24$$

Tangohia te 24 mai i ngā taha e rua.

$$-4m^{2}+4m+48-24=0$$

Tangohia te 24 i te 48, ka 24.

$$-4m^{2}+4m+24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 4 mō b, me 24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-4±\sqrt{4^{2}-4\left(-4\right)\times 24}}{2\left(-4\right)}$$

Pūrua 4.

$$m=\frac{-4±\sqrt{16-4\left(-4\right)\times 24}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$m=\frac{-4±\sqrt{16+16\times 24}}{2\left(-4\right)}$$

Whakareatia 16 ki te 24.

$$m=\frac{-4±\sqrt{16+384}}{2\left(-4\right)}$$

Tāpiri 16 ki te 384.

$$m=\frac{-4±\sqrt{400}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 400.

$$m=\frac{-4±20}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$m=\frac{-4±20}{-8}$$

Nā, me whakaoti te whārite m=\frac{-4±20}{-8} ina he tāpiri te ±. Tāpiri -4 ki te 20.

$$m=\frac{16}{-8}$$

Whakawehe 16 ki te -8.

$$m=-2$$

Nā, me whakaoti te whārite m=\frac{-4±20}{-8} ina he tango te ±. Tango 20 mai i -4.

$$m=-\frac{24}{-8}$$

Whakawehe -24 ki te -8.

$$m=3$$

Kua oti te whārite te whakatau.

$$m=-2 m=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe m ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(m-2\right)^{2}.

$$2\left(m-6\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te m-6.

$$\left(2m-12\right)\left(m-4\right)=6\left(m-2\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2m-12 ki te m-4 ka whakakotahi i ngā kupu rite.

$$2m^{2}-20m+48=6\left(m-2\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(m-2\right)^{2}.

$$2m^{2}-20m+48=6\left(m^{2}-4m+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te m^{2}-4m+4.

$$2m^{2}-20m+48=6m^{2}-24m+24$$

Tangohia te 6m^{2} mai i ngā taha e rua.

$$2m^{2}-20m+48-6m^{2}=-24m+24$$

Pahekotia te 2m^{2} me -6m^{2}, ka -4m^{2}.

$$-4m^{2}-20m+48=-24m+24$$

Me tāpiri te 24m ki ngā taha e rua.

$$-4m^{2}-20m+48+24m=24$$

Pahekotia te -20m me 24m, ka 4m.

$$-4m^{2}+4m+48=24$$

Tangohia te 48 mai i ngā taha e rua.

$$-4m^{2}+4m=24-48$$

Tangohia te 48 i te 24, ka -24.

$$-4m^{2}+4m=-24$$

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4m^{2}+4m}{-4}=-\frac{24}{-4}$$

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

$$m^{2}+\frac{4}{-4}m=-\frac{24}{-4}$$

Whakawehe 4 ki te -4.

$$m^{2}-m=-\frac{24}{-4}$$

Whakawehe -24 ki te -4.

$$m^{2}-m=6$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-m+\left(-\frac{1}{2}\right)^{2}=6+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-m+\frac{1}{4}=6+\frac{1}{4}$$

Tāpiri 6 ki te \frac{1}{4}.

$$m^{2}-m+\frac{1}{4}=\frac{25}{4}$$

Tauwehea m^{2}-m+\frac{1}{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}.

$$\left(m-\frac{1}{2}\right)^{2}=\frac{25}{4}$$

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

$$\sqrt{\left(m-\frac{1}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$m-\frac{1}{2}=\frac{5}{2} m-\frac{1}{2}=-\frac{5}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$m=3 m=-2$$