Whakaoti i te sqrt{2x+16}=2x+4

$$\sqrt { 2 x + 16 } = 2 x + 4$$

Whakaoti mō x

$$x=0$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+16}\right)^{2}=\left(2x+4\right)^{2}$$

Tātaihia te \sqrt{2x+16} mā te pū o 2, kia riro ko 2x+16.

$$2x+16=\left(2x+4\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+4\right)^{2}.

$$2x+16=4x^{2}+16x+16$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$2x+16-4x^{2}=16x+16$$

Tangohia te 16x mai i ngā taha e rua.

$$2x+16-4x^{2}-16x=16$$

Pahekotia te 2x me -16x, ka -14x.

$$-14x+16-4x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$-14x+16-4x^{2}-16=0$$

Tangohia te 16 i te 16, ka 0.

$$-14x-4x^{2}=0$$

Tauwehea te x.

$$x\left(-14-4x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -14-4x=0.

$$x=0 x=-\frac{7}{2}$$

Whakakapia te 0 mō te x i te whārite \sqrt{2x+16}=2x+4.

$$\sqrt{2\times 0+16}=2\times 0+4$$

Whakarūnātia. Ko te uara x=0 kua ngata te whārite.

$$4=4$$

Whakakapia te -\frac{7}{2} mō te x i te whārite \sqrt{2x+16}=2x+4.

$$\sqrt{2\left(-\frac{7}{2}\right)+16}=2\left(-\frac{7}{2}\right)+4$$

Whakarūnātia. Ko te uara x=-\frac{7}{2} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$3=-3$$

Ko te whārite \sqrt{2x+16}=2x+4 he rongoā ahurei.

$$x=0$$