Whakaoti i te sqrt{x+5}+sqrt{x}=5

$$\sqrt { x + 5 } + \sqrt { x } = 5$$

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

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

$$\sqrt{x+5}=5-\sqrt{x}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+5}\right)^{2}=\left(5-\sqrt{x}\right)^{2}$$

Tātaihia te \sqrt{x+5} mā te pū o 2, kia riro ko x+5.

$$x+5=\left(5-\sqrt{x}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5-\sqrt{x}\right)^{2}.

$$x+5=25-10\sqrt{x}+\left(\sqrt{x}\right)^{2}$$

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

$$x+5=25-10\sqrt{x}+x$$

Me tāpiri te 10\sqrt{x} ki ngā taha e rua.

$$x+5+10\sqrt{x}=25+x$$

Tangohia te x mai i ngā taha e rua.

$$x+5+10\sqrt{x}-x=25$$

Pahekotia te x me -x, ka 0.

$$5+10\sqrt{x}=25$$

Tangohia te 5 mai i ngā taha e rua.

$$10\sqrt{x}=25-5$$

Tangohia te 5 i te 25, ka 20.

$$10\sqrt{x}=20$$

Whakawehea ngā taha e rua ki te 10.

$$\sqrt{x}=\frac{20}{10}$$

Whakawehea te 20 ki te 10, kia riro ko 2.

$$\sqrt{x}=2$$

Pūruatia ngā taha e rua o te whārite.

$$x=4$$

Whakakapia te 4 mō te x i te whārite \sqrt{x+5}+\sqrt{x}=5.

$$\sqrt{4+5}+\sqrt{4}=5$$

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$5=5$$

Ko te whārite \sqrt{x+5}=-\sqrt{x}+5 he rongoā ahurei.

$$x=4$$