Whakaoti i te 1/2x+x=51/x

$$\frac{ 1 }{ 2 } x+x = \frac{ 51 }{ x }$$

Whakaoti mō x

$$x=\sqrt{34}\approx 5.830951895$$

$$x=-\sqrt{34}\approx -5.830951895$$

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 2x, arā, te tauraro pātahi he tino iti rawa te kitea o 2,x.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

Me whakakore te 2 me te 2.

$$xx+2xx=2\times 51$$

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

$$x^{2}+2xx=2\times 51$$

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

$$x^{2}+2x^{2}=2\times 51$$

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

$$3x^{2}=2\times 51$$

Whakareatia te 2 ki te 51, ka 102.

$$3x^{2}=102$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{102}{3}$$

Whakawehea te 102 ki te 3, kia riro ko 34.

$$x^{2}=34$$

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

$$x=\sqrt{34} x=-\sqrt{34}$$

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 2x, arā, te tauraro pātahi he tino iti rawa te kitea o 2,x.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

Me whakakore te 2 me te 2.

$$xx+2xx=2\times 51$$

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

$$x^{2}+2xx=2\times 51$$

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

$$x^{2}+2x^{2}=2\times 51$$

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

$$3x^{2}=2\times 51$$

Whakareatia te 2 ki te 51, ka 102.

$$3x^{2}=102$$

Tangohia te 102 mai i ngā taha e rua.

$$3x^{2}-102=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -102 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-102\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-102\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-102\right)}}{2\times 3}$$

Whakareatia -12 ki te -102.

$$x=\frac{0±\sqrt{1224}}{2\times 3}$$

Tuhia te pūtakerua o te 1224.

$$x=\frac{0±6\sqrt{34}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±6\sqrt{34}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{34}}{6} ina he tāpiri te ±.

$$x=\sqrt{34}$$

Nā, me whakaoti te whārite x=\frac{0±6\sqrt{34}}{6} ina he tango te ±.

$$x=-\sqrt{34}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{34} x=-\sqrt{34}$$