Whakaoti i te frac{2sqrt{x}+1}{3}=x

$$\frac { 2 \sqrt { x } + 1 } { 3 } = x$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Whakawehea ia wā o 2\sqrt{x}+1 ki te 3, kia riro ko \frac{2}{3}\sqrt{x}+\frac{1}{3}.

$$\frac{2}{3}\sqrt{x}+\frac{1}{3}=x$$

Tangohia te x mai i ngā taha e rua.

$$\frac{2}{3}\sqrt{x}+\frac{1}{3}-x=0$$

Tangohia te \frac{1}{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$\frac{2}{3}\sqrt{x}-x=-\frac{1}{3}$$

Me tango -x mai i ngā taha e rua o te whārite.

$$\frac{2}{3}\sqrt{x}=-\frac{1}{3}+x$$

Pūruatia ngā taha e rua o te whārite.

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

Whakarohaina te \left(\frac{2}{3}\sqrt{x}\right)^{2}.

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

Tātaihia te \frac{2}{3} mā te pū o 2, kia riro ko \frac{4}{9}.

$$\frac{4}{9}\left(\sqrt{x}\right)^{2}=\left(-\frac{1}{3}+x\right)^{2}$$

Tātaihia te \sqrt{x} mā te pū o 2, kia riro ko x.

$$\frac{4}{9}x=\left(-\frac{1}{3}+x\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-\frac{1}{3}+x\right)^{2}.

$$\frac{4}{9}x=\frac{1}{9}-\frac{2}{3}x+x^{2}$$

Me tāpiri te \frac{2}{3}x ki ngā taha e rua.

$$\frac{4}{9}x+\frac{2}{3}x=\frac{1}{9}+x^{2}$$

Pahekotia te \frac{4}{9}x me \frac{2}{3}x, ka \frac{10}{9}x.

$$\frac{10}{9}x=\frac{1}{9}+x^{2}$$

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

$$\frac{10}{9}x-x^{2}=\frac{1}{9}$$

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.

$$-x^{2}+\frac{10}{9}x=\frac{1}{9}$$

Me tango \frac{1}{9} mai i ngā taha e rua o te whārite.

$$-x^{2}+\frac{10}{9}x-\frac{1}{9}=\frac{1}{9}-\frac{1}{9}$$

Mā te tango i te \frac{1}{9} i a ia ake anō ka toe ko te 0.

$$-x^{2}+\frac{10}{9}x-\frac{1}{9}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, \frac{10}{9} mō b, me -\frac{1}{9} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{10}{9}±\sqrt{\left(\frac{10}{9}\right)^{2}-4\left(-1\right)\left(-\frac{1}{9}\right)}}{2\left(-1\right)}$$

Pūruatia \frac{10}{9} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\frac{10}{9}±\sqrt{\frac{100}{81}-4\left(-1\right)\left(-\frac{1}{9}\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\frac{10}{9}±\sqrt{\frac{100}{81}+4\left(-\frac{1}{9}\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -\frac{1}{9}.

$$x=\frac{-\frac{10}{9}±\sqrt{\frac{100}{81}-\frac{4}{9}}}{2\left(-1\right)}$$

Tāpiri \frac{100}{81} ki te -\frac{4}{9} 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.

$$x=\frac{-\frac{10}{9}±\sqrt{\frac{64}{81}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \frac{64}{81}.

$$x=\frac{-\frac{10}{9}±\frac{8}{9}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-\frac{10}{9}±\frac{8}{9}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-\frac{10}{9}±\frac{8}{9}}{-2} ina he tāpiri te ±. Tāpiri -\frac{10}{9} ki te \frac{8}{9} 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.

$$x=-\frac{\frac{2}{9}}{-2}$$

Whakawehe -\frac{2}{9} ki te -2.

$$x=\frac{1}{9}$$

Nā, me whakaoti te whārite x=\frac{-\frac{10}{9}±\frac{8}{9}}{-2} ina he tango te ±. Tango \frac{8}{9} mai i -\frac{10}{9} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Whakawehe -2 ki te -2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{9} x=1$$

Whakakapia te \frac{1}{9} mō te x i te whārite \frac{2\sqrt{x}+1}{3}=x.

$$\frac{2\sqrt{\frac{1}{9}}+1}{3}=\frac{1}{9}$$

Whakarūnātia. Ko te uara x=\frac{1}{9} kāore e ngata ana ki te whārite.

$$\frac{5}{9}=\frac{1}{9}$$

Whakakapia te 1 mō te x i te whārite \frac{2\sqrt{x}+1}{3}=x.

$$\frac{2\sqrt{1}+1}{3}=1$$

Whakarūnātia. Ko te uara x=1 kua ngata te whārite.

$$1=1$$

Ko te whārite \frac{2\sqrt{x}}{3}=x-\frac{1}{3} he rongoā ahurei.

$$x=1$$