Whakaoti i te 5x+2/5x=5

$$5 x + \frac { 2 } { 5 x } = 5$$

Whakaoti mō x

$$x=-\frac{\sqrt{17}}{10}+\frac{1}{2}\approx 0.087689437$$

$$x=\frac{\sqrt{17}}{10}+\frac{1}{2}\approx 0.912310563$$

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 5x.

$$5x\times 5x+2=25x$$

Whakareatia te 5 ki te 5, ka 25.

$$25xx+2=25x$$

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

$$25x^{2}+2=25x$$

Tangohia te 25x mai i ngā taha e rua.

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

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.

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

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

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

Pūrua -25.

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

Whakareatia -4 ki te 25.

$$x=\frac{-\left(-25\right)±\sqrt{625-100\times 2}}{2\times 25}$$

Whakareatia -100 ki te 2.

$$x=\frac{-\left(-25\right)±\sqrt{625-200}}{2\times 25}$$

Tāpiri 625 ki te -200.

$$x=\frac{-\left(-25\right)±\sqrt{425}}{2\times 25}$$

Tuhia te pūtakerua o te 425.

$$x=\frac{-\left(-25\right)±5\sqrt{17}}{2\times 25}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±5\sqrt{17}}{2\times 25}$$

Whakareatia 2 ki te 25.

$$x=\frac{25±5\sqrt{17}}{50}$$

Nā, me whakaoti te whārite x=\frac{25±5\sqrt{17}}{50} ina he tāpiri te ±. Tāpiri 25 ki te 5\sqrt{17}.

$$x=\frac{5\sqrt{17}+25}{50}$$

Whakawehe 25+5\sqrt{17} ki te 50.

$$x=\frac{\sqrt{17}}{10}+\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{25±5\sqrt{17}}{50} ina he tango te ±. Tango 5\sqrt{17} mai i 25.

$$x=\frac{25-5\sqrt{17}}{50}$$

Whakawehe 25-5\sqrt{17} ki te 50.

$$x=-\frac{\sqrt{17}}{10}+\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{17}}{10}+\frac{1}{2} x=-\frac{\sqrt{17}}{10}+\frac{1}{2}$$

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 5x.

$$5x\times 5x+2=25x$$

Whakareatia te 5 ki te 5, ka 25.

$$25xx+2=25x$$

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

$$25x^{2}+2=25x$$

Tangohia te 25x mai i ngā taha e rua.

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

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakawehea ngā taha e rua ki te 25.

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

Mā te whakawehe ki te 25 ka wetekia te whakareanga ki te 25.

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

Whakawehe -25 ki te 25.

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

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.

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

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

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

Tāpiri -\frac{2}{25} ki te \frac{1}{4} 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.

$$x^{2}-x+\frac{1}{4}=\frac{17}{100}$$

Tauwehea x^{2}-x+\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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{17}{100}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{17}{100}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{\sqrt{17}}{10} x-\frac{1}{2}=-\frac{\sqrt{17}}{10}$$

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

$$x=\frac{\sqrt{17}}{10}+\frac{1}{2} x=-\frac{\sqrt{17}}{10}+\frac{1}{2}$$