Whakaoti i te sqrt{z}-7=sqrt{z-105}

$$\sqrt { z } - 7 = \sqrt { z - 105 }$$

Whakaoti mō z

$$z=121$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{z}-7\right)^{2}=\left(\sqrt{z-105}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{z}-7\right)^{2}.

$$\left(\sqrt{z}\right)^{2}-14\sqrt{z}+49=\left(\sqrt{z-105}\right)^{2}$$

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

$$z-14\sqrt{z}+49=\left(\sqrt{z-105}\right)^{2}$$

Tātaihia te \sqrt{z-105} mā te pū o 2, kia riro ko z-105.

$$z-14\sqrt{z}+49=z-105$$

Tangohia te z mai i ngā taha e rua.

$$z-14\sqrt{z}+49-z=-105$$

Pahekotia te z me -z, ka 0.

$$-14\sqrt{z}+49=-105$$

Tangohia te 49 mai i ngā taha e rua.

$$-14\sqrt{z}=-105-49$$

Tangohia te 49 i te -105, ka -154.

$$-14\sqrt{z}=-154$$

Whakawehea ngā taha e rua ki te -14.

$$\sqrt{z}=\frac{-154}{-14}$$

Whakawehea te -154 ki te -14, kia riro ko 11.

$$\sqrt{z}=11$$

Pūruatia ngā taha e rua o te whārite.

$$z=121$$

Whakakapia te 121 mō te z i te whārite \sqrt{z}-7=\sqrt{z-105}.

$$\sqrt{121}-7=\sqrt{121-105}$$

Whakarūnātia. Ko te uara z=121 kua ngata te whārite.

$$4=4$$

Ko te whārite \sqrt{z}-7=\sqrt{z-105} he rongoā ahurei.

$$z=121$$