Whakaoti i te a^2=25/121

$$a ^ { 2 } = \frac { 25 } { 121 }$$

Whakaoti mō a

$$a=\frac{5}{11}\approx 0.454545455$$

$$a=-\frac{5}{11}\approx -0.454545455$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te \frac{25}{121} mai i ngā taha e rua.

$$a^{2}-\frac{25}{121}=0$$

Me whakarea ngā taha e rua ki te 121.

$$121a^{2}-25=0$$

Whakaarohia te 121a^{2}-25. Tuhia anō te 121a^{2}-25 hei \left(11a\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).

$$\left(11a-5\right)\left(11a+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 11a-5=0 me te 11a+5=0.

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Ngā Upane mā te Kimi Pūtakerua

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

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{25}{121} mai i ngā taha e rua.

$$a^{2}-\frac{25}{121}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{25}{121} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{121}\right)}}{2}$$

Pūrua 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{25}{121}\right)}}{2}$$

Whakareatia -4 ki te -\frac{25}{121}.

$$a=\frac{0±\sqrt{\frac{100}{121}}}{2}$$

Tuhia te pūtakerua o te \frac{100}{121}.

$$a=\frac{0±\frac{10}{11}}{2}$$

Nā, me whakaoti te whārite a=\frac{0±\frac{10}{11}}{2} ina he tāpiri te ±.

$$a=\frac{5}{11}$$

Nā, me whakaoti te whārite a=\frac{0±\frac{10}{11}}{2} ina he tango te ±.

$$a=-\frac{5}{11}$$

Kua oti te whārite te whakatau.

$$a=\frac{5}{11} a=-\frac{5}{11}$$