Whakaoti i te 81x^2=25

$$81 x ^ { 2 } = 25$$

Whakaoti mō x

$$x=\frac{5}{9}\approx 0.555555556$$

$$x=-\frac{5}{9}\approx -0.555555556$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 81.

$$x^{2}=\frac{25}{81}$$

Tangohia te \frac{25}{81} mai i ngā taha e rua.

$$x^{2}-\frac{25}{81}=0$$

Me whakarea ngā taha e rua ki te 81.

$$81x^{2}-25=0$$

Whakaarohia te 81x^{2}-25. Tuhia anō te 81x^{2}-25 hei \left(9x\right)^{2}-5^{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).

$$\left(9x-5\right)\left(9x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 9x-5=0 me te 9x+5=0.

$$x=\frac{5}{9} x=-\frac{5}{9}$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 81.

$$x^{2}=\frac{25}{81}$$

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

$$x=\frac{5}{9} x=-\frac{5}{9}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 81.

$$x^{2}=\frac{25}{81}$$

Tangohia te \frac{25}{81} mai i ngā taha e rua.

$$x^{2}-\frac{25}{81}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{25}{81} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{81}\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{25}{81}\right)}}{2}$$

Whakareatia -4 ki te -\frac{25}{81}.

$$x=\frac{0±\sqrt{\frac{100}{81}}}{2}$$

Tuhia te pūtakerua o te \frac{100}{81}.

$$x=\frac{0±\frac{10}{9}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{10}{9}}{2} ina he tāpiri te ±.

$$x=\frac{5}{9}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{10}{9}}{2} ina he tango te ±.

$$x=-\frac{5}{9}$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{9} x=-\frac{5}{9}$$