Whakaoti i te x/4=8/x

$$\frac { x } { 4 } = \frac { 8 } { x }$$

Whakaoti mō x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

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 4x, arā, te tauraro pātahi he tino iti rawa te kitea o 4,x.

$$xx=4\times 8$$

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

$$x^{2}=4\times 8$$

Whakareatia te 4 ki te 8, ka 32.

$$x^{2}=32$$

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

$$x=4\sqrt{2} x=-4\sqrt{2}$$

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 4x, arā, te tauraro pātahi he tino iti rawa te kitea o 4,x.

$$xx=4\times 8$$

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

$$x^{2}=4\times 8$$

Whakareatia te 4 ki te 8, ka 32.

$$x^{2}=32$$

Tangohia te 32 mai i ngā taha e rua.

$$x^{2}-32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-32\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-32\right)}}{2}$$

Whakareatia -4 ki te -32.

$$x=\frac{0±\sqrt{128}}{2}$$

Tuhia te pūtakerua o te 128.

$$x=\frac{0±8\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{2}}{2} ina he tāpiri te ±.

$$x=4\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{2}}{2} ina he tango te ±.

$$x=-4\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{2} x=-4\sqrt{2}$$