Whakaoti i te 2x/1x-x/2+x+1/4=6x

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

Whakaoti mō x

$$x = \frac{\sqrt{593} + 25}{16} \approx 3.084474458$$

$$x=\frac{25-\sqrt{593}}{16}\approx 0.040525542$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 4, arā, te tauraro pātahi he tino iti rawa te kitea o 2,4.

$$4\times 2xx-2x+x+1=24x$$

Whakareatia te 4 ki te 2, ka 8.

$$8xx-2x+x+1=24x$$

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

$$8x^{2}-2x+x+1=24x$$

Pahekotia te -2x me x, ka -x.

$$8x^{2}-x+1=24x$$

Tangohia te 24x mai i ngā taha e rua.

$$8x^{2}-x+1-24x=0$$

Pahekotia te -x me -24x, ka -25x.

$$8x^{2}-25x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -25 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 8}}{2\times 8}$$

Pūrua -25.

$$x=\frac{-\left(-25\right)±\sqrt{625-4\times 8}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-\left(-25\right)±\sqrt{625-32}}{2\times 8}$$

Tāpiri 625 ki te -32.

$$x=\frac{-\left(-25\right)±\sqrt{593}}{2\times 8}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±\sqrt{593}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{25±\sqrt{593}}{16}$$

Nā, me whakaoti te whārite x=\frac{25±\sqrt{593}}{16} ina he tāpiri te ±. Tāpiri 25 ki te \sqrt{593}.

$$x=\frac{\sqrt{593}+25}{16}$$

Nā, me whakaoti te whārite x=\frac{25±\sqrt{593}}{16} ina he tango te ±. Tango \sqrt{593} mai i 25.

$$x=\frac{25-\sqrt{593}}{16}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{593}+25}{16} x=\frac{25-\sqrt{593}}{16}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 4, arā, te tauraro pātahi he tino iti rawa te kitea o 2,4.

$$4\times 2xx-2x+x+1=24x$$

Whakareatia te 4 ki te 2, ka 8.

$$8xx-2x+x+1=24x$$

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

$$8x^{2}-2x+x+1=24x$$

Pahekotia te -2x me x, ka -x.

$$8x^{2}-x+1=24x$$

Tangohia te 24x mai i ngā taha e rua.

$$8x^{2}-x+1-24x=0$$

Pahekotia te -x me -24x, ka -25x.

$$8x^{2}-25x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$8x^{2}-25x=-1$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-25x}{8}=-\frac{1}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}-\frac{25}{8}x=-\frac{1}{8}$$

Whakawehea te -\frac{25}{8}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{25}{16}. Nā, tāpiria te pūrua o te -\frac{25}{16} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{25}{8}x+\left(-\frac{25}{16}\right)^{2}=-\frac{1}{8}+\left(-\frac{25}{16}\right)^{2}$$

Pūruatia -\frac{25}{16} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{25}{8}x+\frac{625}{256}=-\frac{1}{8}+\frac{625}{256}$$

Tāpiri -\frac{1}{8} ki te \frac{625}{256} 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.

$$x^{2}-\frac{25}{8}x+\frac{625}{256}=\frac{593}{256}$$

Tauwehea x^{2}-\frac{25}{8}x+\frac{625}{256}. 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}.

$$\left(x-\frac{25}{16}\right)^{2}=\frac{593}{256}$$

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

$$\sqrt{\left(x-\frac{25}{16}\right)^{2}}=\sqrt{\frac{593}{256}}$$

Whakarūnātia.

$$x-\frac{25}{16}=\frac{\sqrt{593}}{16} x-\frac{25}{16}=-\frac{\sqrt{593}}{16}$$

Me tāpiri \frac{25}{16} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{593}+25}{16} x=\frac{25-\sqrt{593}}{16}$$