Whakaoti i te (2sqrt{2})^2=(sqrt{3}x)^2+x^2-2sqrt{3}x*x*frac{sqrt{3}}{3}

$$( 2 \sqrt { 2 } ) ^ { 2 } = ( \sqrt { 3 } x ) ^ { 2 } + x ^ { 2 } - 2 \sqrt { 3 } x \cdot x \cdot \frac { \sqrt { 3 } } { 3 }$$

Whakaoti mō x

$$x=2$$

$$x=-2$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

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

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

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

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

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 4 ki te 2, ka 8.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

Whakareatia te 3 ki te 8, ka 24.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

Pahekotia te 3x^{2} me x^{2}, ka 4x^{2}.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

Whakareatia te 3 ki te 4, ka 12.

$$24=12x^{2}-2\times 3x^{2}$$

Whakareatia te 2 ki te 3, ka 6.

$$24=12x^{2}-6x^{2}$$

Pahekotia te 12x^{2} me -6x^{2}, ka 6x^{2}.

$$24=6x^{2}$$

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

$$6x^{2}=24$$

Tangohia te 24 mai i ngā taha e rua.

$$6x^{2}-24=0$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}-4=0$$

Whakaarohia te x^{2}-4. Tuhia anō te x^{2}-4 hei x^{2}-2^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te x+2=0.

$$x=2 x=-2$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 3.

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

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

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

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

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 4 ki te 2, ka 8.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

Whakareatia te 3 ki te 8, ka 24.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

Pahekotia te 3x^{2} me x^{2}, ka 4x^{2}.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

Whakareatia te 3 ki te 4, ka 12.

$$24=12x^{2}-2\times 3x^{2}$$

Whakareatia te 2 ki te 3, ka 6.

$$24=12x^{2}-6x^{2}$$

Pahekotia te 12x^{2} me -6x^{2}, ka 6x^{2}.

$$24=6x^{2}$$

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

$$6x^{2}=24$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{24}{6}$$

Whakawehea te 24 ki te 6, kia riro ko 4.

$$x^{2}=4$$

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

$$x=2 x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

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

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

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

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

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

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

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Whakareatia te 4 ki te 2, ka 8.

$$3\times 8=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

Whakareatia te 3 ki te 8, ka 24.

$$24=3\left(\left(\sqrt{3}x\right)^{2}+x^{2}\right)-2\times 3x^{2}$$

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

$$24=3\left(\left(\sqrt{3}\right)^{2}x^{2}+x^{2}\right)-2\times 3x^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$24=3\left(3x^{2}+x^{2}\right)-2\times 3x^{2}$$

Pahekotia te 3x^{2} me x^{2}, ka 4x^{2}.

$$24=3\times 4x^{2}-2\times 3x^{2}$$

Whakareatia te 3 ki te 4, ka 12.

$$24=12x^{2}-2\times 3x^{2}$$

Whakareatia te 2 ki te 3, ka 6.

$$24=12x^{2}-6x^{2}$$

Pahekotia te 12x^{2} me -6x^{2}, ka 6x^{2}.

$$24=6x^{2}$$

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

$$6x^{2}=24$$

Tangohia te 24 mai i ngā taha e rua.

$$6x^{2}-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-24\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-24\right)}}{2\times 6}$$

Whakareatia -24 ki te -24.

$$x=\frac{0±\sqrt{576}}{2\times 6}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{0±24}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±24}{12}$$

Nā, me whakaoti te whārite x=\frac{0±24}{12} ina he tāpiri te ±. Whakawehe 24 ki te 12.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{0±24}{12} ina he tango te ±. Whakawehe -24 ki te 12.

$$x=-2$$

Kua oti te whārite te whakatau.

$$x=2 x=-2$$