Whakaoti i te sqrt{x+9}+sqrt{x+2}=7

$$\sqrt { x + 9 } + \sqrt { x + 2 } = 7$$

Whakaoti mō x

$$x=7$$

Ngā Upane Otinga

Me tango \sqrt{x+2} mai i ngā taha e rua o te whārite.

$$\sqrt{x+9}=7-\sqrt{x+2}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+9}\right)^{2}=\left(7-\sqrt{x+2}\right)^{2}$$

Tātaihia te \sqrt{x+9} mā te pū o 2, kia riro ko x+9.

$$x+9=\left(7-\sqrt{x+2}\right)^{2}$$

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

$$x+9=49-14\sqrt{x+2}+\left(\sqrt{x+2}\right)^{2}$$

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

$$x+9=49-14\sqrt{x+2}+x+2$$

Tāpirihia te 49 ki te 2, ka 51.

$$x+9=51-14\sqrt{x+2}+x$$

Me tāpiri te 14\sqrt{x+2} ki ngā taha e rua.

$$x+9+14\sqrt{x+2}=51+x$$

Tangohia te x mai i ngā taha e rua.

$$x+9+14\sqrt{x+2}-x=51$$

Pahekotia te x me -x, ka 0.

$$9+14\sqrt{x+2}=51$$

Tangohia te 9 mai i ngā taha e rua.

$$14\sqrt{x+2}=51-9$$

Tangohia te 9 i te 51, ka 42.

$$14\sqrt{x+2}=42$$

Whakawehea ngā taha e rua ki te 14.

$$\sqrt{x+2}=\frac{42}{14}$$

Whakawehea te 42 ki te 14, kia riro ko 3.

$$\sqrt{x+2}=3$$

Pūruatia ngā taha e rua o te whārite.

$$x+2=9$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x+2-2=9-2$$

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

$$x=9-2$$

Tango 2 mai i 9.

$$x=7$$

Whakakapia te 7 mō te x i te whārite \sqrt{x+9}+\sqrt{x+2}=7.

$$\sqrt{7+9}+\sqrt{7+2}=7$$

Whakarūnātia. Ko te uara x=7 kua ngata te whārite.

$$7=7$$

Ko te whārite \sqrt{x+9}=-\sqrt{x+2}+7 he rongoā ahurei.

$$x=7$$