Whakaoti i te sqrt{y^2-y+2}+y=1

$$\sqrt { y ^ { 2 } - y + 2 } + y = 1$$

Whakaoti mō y

$$y=-1$$

Ngā Upane Otinga

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

$$\sqrt{y^{2}-y+2}=1-y$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{y^{2}-y+2}\right)^{2}=\left(1-y\right)^{2}$$

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

$$y^{2}-y+2=\left(1-y\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(1-y\right)^{2}.

$$y^{2}-y+2=1-2y+y^{2}$$

Me tāpiri te 2y ki ngā taha e rua.

$$y^{2}-y+2+2y=1+y^{2}$$

Pahekotia te -y me 2y, ka y.

$$y^{2}+y+2=1+y^{2}$$

Tangohia te y^{2} mai i ngā taha e rua.

$$y^{2}+y+2-y^{2}=1$$

Pahekotia te y^{2} me -y^{2}, ka 0.

$$y+2=1$$

Tangohia te 2 mai i ngā taha e rua.

$$y=1-2$$

Tangohia te 2 i te 1, ka -1.

$$y=-1$$

Whakakapia te -1 mō te y i te whārite \sqrt{y^{2}-y+2}+y=1.

$$\sqrt{\left(-1\right)^{2}-\left(-1\right)+2}-1=1$$

Whakarūnātia. Ko te uara y=-1 kua ngata te whārite.

$$1=1$$

Ko te whārite \sqrt{y^{2}-y+2}=1-y he rongoā ahurei.

$$y=-1$$