Whakaoti i te 7x+1=6/x

$$7 x + 1 = \frac { 6 } { x }$$

Whakaoti mō x

$$x=-1$$

$$x=\frac{6}{7}\approx 0.857142857$$

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.

$$7xx+x=6$$

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

$$7x^{2}+x=6$$

Tangohia te 6 mai i ngā taha e rua.

$$7x^{2}+x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, 1 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 7\left(-6\right)}}{2\times 7}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 7\left(-6\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{-1±\sqrt{1-28\left(-6\right)}}{2\times 7}$$

Whakareatia -28 ki te -6.

$$x=\frac{-1±\sqrt{1+168}}{2\times 7}$$

Tāpiri 1 ki te 168.

$$x=\frac{-1±\sqrt{169}}{2\times 7}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-1±13}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{-1±13}{14}$$

Nā, me whakaoti te whārite x=\frac{-1±13}{14} ina he tāpiri te ±. Tāpiri -1 ki te 13.

$$x=\frac{12}{14}$$

Whakahekea te hautanga \frac{12}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{6}{7}$$

Nā, me whakaoti te whārite x=\frac{-1±13}{14} ina he tango te ±. Tango 13 mai i -1.

$$x=-\frac{14}{14}$$

Whakawehe -14 ki te 14.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=\frac{6}{7} x=-1$$

Ngā Upane mō te Whakaoti i te 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.

$$7xx+x=6$$

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

$$7x^{2}+x=6$$

Whakawehea ngā taha e rua ki te 7.

$$\frac{7x^{2}+x}{7}=\frac{6}{7}$$

Mā te whakawehe ki te 7 ka wetekia te whakareanga ki te 7.

$$x^{2}+\frac{1}{7}x=\frac{6}{7}$$

Whakawehea te \frac{1}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{14}. Nā, tāpiria te pūrua o te \frac{1}{14} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{7}x+\left(\frac{1}{14}\right)^{2}=\frac{6}{7}+\left(\frac{1}{14}\right)^{2}$$

Pūruatia \frac{1}{14} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{7}x+\frac{1}{196}=\frac{6}{7}+\frac{1}{196}$$

Tāpiri \frac{6}{7} ki te \frac{1}{196} 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.

$$x^{2}+\frac{1}{7}x+\frac{1}{196}=\frac{169}{196}$$

Tauwehea x^{2}+\frac{1}{7}x+\frac{1}{196}. 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}.

$$\left(x+\frac{1}{14}\right)^{2}=\frac{169}{196}$$

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

$$\sqrt{\left(x+\frac{1}{14}\right)^{2}}=\sqrt{\frac{169}{196}}$$

Whakarūnātia.

$$x+\frac{1}{14}=\frac{13}{14} x+\frac{1}{14}=-\frac{13}{14}$$

Me tango \frac{1}{14} mai i ngā taha e rua o te whārite.

$$x=\frac{6}{7} x=-1$$