Whakaoti i te 75/x=x+2/3x

$$\frac { 75 } { x } = x + \frac { 2 } { 3 } x$$

Whakaoti mō x

$$x=3\sqrt{5}\approx 6.708203932$$

$$x=-3\sqrt{5}\approx -6.708203932$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3\times 75=3xx+\frac{2}{3}x\times 3x$$

Whakareatia te 3 ki te 75, ka 225.

$$225=3xx+\frac{2}{3}x\times 3x$$

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

$$225=3x^{2}+\frac{2}{3}x\times 3x$$

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

$$225=3x^{2}+\frac{2}{3}x^{2}\times 3$$

Me whakakore te 3 me te 3.

$$225=3x^{2}+2x^{2}$$

Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.

$$225=5x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5x^{2}=225$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{225}{5}$$

Whakawehea te 225 ki te 5, kia riro ko 45.

$$x^{2}=45$$

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

$$x=3\sqrt{5} x=-3\sqrt{5}$$

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. Me whakarea ngā taha e rua o te whārite ki te 3x, arā, te tauraro pātahi he tino iti rawa te kitea o x,3.

$$3\times 75=3xx+\frac{2}{3}x\times 3x$$

Whakareatia te 3 ki te 75, ka 225.

$$225=3xx+\frac{2}{3}x\times 3x$$

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

$$225=3x^{2}+\frac{2}{3}x\times 3x$$

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

$$225=3x^{2}+\frac{2}{3}x^{2}\times 3$$

Me whakakore te 3 me te 3.

$$225=3x^{2}+2x^{2}$$

Pahekotia te 3x^{2} me 2x^{2}, ka 5x^{2}.

$$225=5x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5x^{2}=225$$

Tangohia te 225 mai i ngā taha e rua.

$$5x^{2}-225=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -225 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-225\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-225\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-225\right)}}{2\times 5}$$

Whakareatia -20 ki te -225.

$$x=\frac{0±\sqrt{4500}}{2\times 5}$$

Tuhia te pūtakerua o te 4500.

$$x=\frac{0±30\sqrt{5}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±30\sqrt{5}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{5}}{10} ina he tāpiri te ±.

$$x=3\sqrt{5}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{5}}{10} ina he tango te ±.

$$x=-3\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{5} x=-3\sqrt{5}$$