Whakaoti i te 1/2=frac{sqrt{a^2-3}}{a}

$$\frac { 1 } { 2 } = \frac { \sqrt { a ^ { 2 } - 3 } } { a }$$

Whakaoti mō a

$$a=2$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2a, arā, te tauraro pātahi he tino iti rawa te kitea o 2,a.

$$a=2\sqrt{a^{2}-3}$$

Tangohia te 2\sqrt{a^{2}-3} mai i ngā taha e rua.

$$a-2\sqrt{a^{2}-3}=0$$

Me tango a mai i ngā taha e rua o te whārite.

$$-2\sqrt{a^{2}-3}=-a$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-2\sqrt{a^{2}-3}\right)^{2}=\left(-a\right)^{2}$$

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

$$\left(-2\right)^{2}\left(\sqrt{a^{2}-3}\right)^{2}=\left(-a\right)^{2}$$

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

$$4\left(\sqrt{a^{2}-3}\right)^{2}=\left(-a\right)^{2}$$

Tātaihia te \sqrt{a^{2}-3} mā te pū o 2, kia riro ko a^{2}-3.

$$4\left(a^{2}-3\right)=\left(-a\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te a^{2}-3.

$$4a^{2}-12=\left(-a\right)^{2}$$

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

$$4a^{2}-12=\left(-1\right)^{2}a^{2}$$

Tātaihia te -1 mā te pū o 2, kia riro ko 1.

$$4a^{2}-12=1a^{2}$$

Tangohia te 1a^{2} mai i ngā taha e rua.

$$4a^{2}-12-a^{2}=0$$

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

$$3a^{2}-12=0$$

Whakawehea ngā taha e rua ki te 3.

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

Whakaarohia te a^{2}-4. Tuhia anō te a^{2}-4 hei a^{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).

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

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

$$a=2 a=-2$$

Whakakapia te 2 mō te a i te whārite \frac{1}{2}=\frac{\sqrt{a^{2}-3}}{a}.

$$\frac{1}{2}=\frac{\sqrt{2^{2}-3}}{2}$$

Whakarūnātia. Ko te uara a=2 kua ngata te whārite.

$$\frac{1}{2}=\frac{1}{2}$$

Whakakapia te -2 mō te a i te whārite \frac{1}{2}=\frac{\sqrt{a^{2}-3}}{a}.

$$\frac{1}{2}=\frac{\sqrt{\left(-2\right)^{2}-3}}{-2}$$

Whakarūnātia. Ko te uara a=-2 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$\frac{1}{2}=-\frac{1}{2}$$

Ko te whārite -2\sqrt{a^{2}-3}=-a he rongoā ahurei.

$$a=2$$