Whakaoti i te 1/3x^2=49/3

$$\frac{ 1 }{ 3 } { x }^{ 2 } = \frac{ 49 }{ 3 }$$

Whakaoti mō x

$$x=7$$

$$x=-7$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

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

$$x^{2}=\frac{49}{3}\times 3$$

Whakareatia te \frac{49}{3} ki te 3, ka 49.

$$x^{2}=49$$

Tangohia te 49 mai i ngā taha e rua.

$$x^{2}-49=0$$

Whakaarohia te x^{2}-49. Tuhia anō te x^{2}-49 hei x^{2}-7^{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).

$$\left(x-7\right)\left(x+7\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-7=0 me te x+7=0.

$$x=7 x=-7$$

Ngā Upane mā te Kimi Pūtakerua

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

$$x^{2}=\frac{49}{3}\times 3$$

Whakareatia te \frac{49}{3} ki te 3, ka 49.

$$x^{2}=49$$

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

$$x=7 x=-7$$

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}.

$$x^{2}=\frac{49}{3}\times 3$$

Whakareatia te \frac{49}{3} ki te 3, ka 49.

$$x^{2}=49$$

Tangohia te 49 mai i ngā taha e rua.

$$x^{2}-49=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -49 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

Whakareatia -4 ki te -49.

$$x=\frac{0±\sqrt{196}}{2}$$

Tuhia te pūtakerua o te 196.

$$x=\frac{0±14}{2}$$

Nā, me whakaoti te whārite x=\frac{0±14}{2} ina he tāpiri te ±. Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{0±14}{2} ina he tango te ±. Whakawehe -14 ki te 2.

$$x=-7$$

Kua oti te whārite te whakatau.

$$x=7 x=-7$$