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

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

Whakaoti mō x

$$x=7$$

Ngā Upane Otinga

Me tango \sqrt{x+9} mai i ngā taha e rua o te whārite.

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(7-\sqrt{x+9}\right)^{2}.

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

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

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

Tāpirihia te 49 ki te 9, ka 58.

$$x+2=58-14\sqrt{x+9}+x$$

Me tāpiri te 14\sqrt{x+9} ki ngā taha e rua.

$$x+2+14\sqrt{x+9}=58+x$$

Tangohia te x mai i ngā taha e rua.

$$x+2+14\sqrt{x+9}-x=58$$

Pahekotia te x me -x, ka 0.

$$2+14\sqrt{x+9}=58$$

Tangohia te 2 mai i ngā taha e rua.

$$14\sqrt{x+9}=58-2$$

Tangohia te 2 i te 58, ka 56.

$$14\sqrt{x+9}=56$$

Whakawehea ngā taha e rua ki te 14.

$$\sqrt{x+9}=\frac{56}{14}$$

Whakawehea te 56 ki te 14, kia riro ko 4.

$$\sqrt{x+9}=4$$

Pūruatia ngā taha e rua o te whārite.

$$x+9=16$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$x+9-9=16-9$$

Mā te tango i te 9 i a ia ake anō ka toe ko te 0.

$$x=16-9$$

Tango 9 mai i 16.

$$x=7$$

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

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

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

$$7=7$$

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

$$x=7$$