Whakaoti i te sqrt{y}+sqrt{y+2}=3

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

Whakaoti mō y

$$y = \frac{49}{36} = 1\frac{13}{36} \approx 1.361111111$$

Ngā Upane Otinga

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

$$\sqrt{y}=3-\sqrt{y+2}$$

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

$$y=9-6\sqrt{y+2}+\left(\sqrt{y+2}\right)^{2}$$

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

$$y=9-6\sqrt{y+2}+y+2$$

Tāpirihia te 9 ki te 2, ka 11.

$$y=11-6\sqrt{y+2}+y$$

Me tāpiri te 6\sqrt{y+2} ki ngā taha e rua.

$$y+6\sqrt{y+2}=11+y$$

Tangohia te y mai i ngā taha e rua.

$$y+6\sqrt{y+2}-y=11$$

Pahekotia te y me -y, ka 0.

$$6\sqrt{y+2}=11$$

Whakawehea ngā taha e rua ki te 6.

$$\sqrt{y+2}=\frac{11}{6}$$

Pūruatia ngā taha e rua o te whārite.

$$y+2=\frac{121}{36}$$

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

$$y+2-2=\frac{121}{36}-2$$

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

$$y=\frac{121}{36}-2$$

Tango 2 mai i \frac{121}{36}.

$$y=\frac{49}{36}$$

Whakakapia te \frac{49}{36} mō te y i te whārite \sqrt{y}+\sqrt{y+2}=3.

$$\sqrt{\frac{49}{36}}+\sqrt{\frac{49}{36}+2}=3$$

Whakarūnātia. Ko te uara y=\frac{49}{36} kua ngata te whārite.

$$3=3$$

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

$$y=\frac{49}{36}$$