Whakaoti i te sqrt{3a}-sqrt{2a}=sqrt{a}

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

Whakaoti mō a

$$a=0$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3a}-\sqrt{2a}\right)^{2}.

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

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

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

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

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

Pahekotia te 3a me 2a, ka 5a.

$$5a-2\sqrt{3a}\sqrt{2a}=\left(\sqrt{a}\right)^{2}$$

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

$$5a-2\sqrt{3a}\sqrt{2a}=a$$

Me tango 5a mai i ngā taha e rua o te whārite.

$$-2\sqrt{3a}\sqrt{2a}=a-5a$$

Pahekotia te a me -5a, ka -4a.

$$-2\sqrt{3a}\sqrt{2a}=-4a$$

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

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

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

Whakareatia te 4 ki te 3, ka 12.

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

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

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

Whakareatia te 12 ki te 2, ka 24.

$$24aa=\left(-4a\right)^{2}$$

Whakareatia te a ki te a, ka a^{2}.

$$24a^{2}=\left(-4a\right)^{2}$$

Whakarohaina te \left(-4a\right)^{2}.

$$24a^{2}=\left(-4\right)^{2}a^{2}$$

Tātaihia te -4 mā te pū o 2, kia riro ko 16.

$$24a^{2}=16a^{2}$$

Tangohia te 16a^{2} mai i ngā taha e rua.

$$24a^{2}-16a^{2}=0$$

Pahekotia te 24a^{2} me -16a^{2}, ka 8a^{2}.

$$8a^{2}=0$$

Whakawehea ngā taha e rua ki te 8. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$a^{2}=0$$

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

$$a=0 a=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$a=0$$

Whakakapia te 0 mō te a i te whārite \sqrt{3a}-\sqrt{2a}=\sqrt{a}.

$$\sqrt{3\times 0}-\sqrt{2\times 0}=\sqrt{0}$$

Whakarūnātia. Ko te uara a=0 kua ngata te whārite.

$$0=0$$

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

$$a=0$$