Whakaoti i te 1/3(6x^2-4)=11

$$1 / 3 ( 6 x ^ { 2 } - 4 ) = 11$$

Whakaoti mō x

$$x = \frac{\sqrt{222}}{6} \approx 2.483277404$$

$$x = -\frac{\sqrt{222}}{6} \approx -2.483277404$$

Ngā Upane mā te Kimi Pūtakerua

Me whakarea ngā taha e rua ki te 3, te tau utu o \frac{1}{3}.

$$6x^{2}-4=11\times 3$$

Whakareatia te 11 ki te 3, ka 33.

$$6x^{2}-4=33$$

Me tāpiri te 4 ki ngā taha e rua.

$$6x^{2}=33+4$$

Tāpirihia te 33 ki te 4, ka 37.

$$6x^{2}=37$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{37}{6}$$

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

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 3, te tau utu o \frac{1}{3}.

$$6x^{2}-4=11\times 3$$

Whakareatia te 11 ki te 3, ka 33.

$$6x^{2}-4=33$$

Tangohia te 33 mai i ngā taha e rua.

$$6x^{2}-4-33=0$$

Tangohia te 33 i te -4, ka -37.

$$6x^{2}-37=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me -37 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-37\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-37\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-37\right)}}{2\times 6}$$

Whakareatia -24 ki te -37.

$$x=\frac{0±\sqrt{888}}{2\times 6}$$

Tuhia te pūtakerua o te 888.

$$x=\frac{0±2\sqrt{222}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±2\sqrt{222}}{12}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{222}}{12} ina he tāpiri te ±.

$$x=\frac{\sqrt{222}}{6}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{222}}{12} ina he tango te ±.

$$x=-\frac{\sqrt{222}}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{222}}{6} x=-\frac{\sqrt{222}}{6}$$