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

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

Whakaoti mō x

$$x=9$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

$$16+x=x^{2}-8x+16$$

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

$$16+x-x^{2}=-8x+16$$

Me tāpiri te 8x ki ngā taha e rua.

$$16+x-x^{2}+8x=16$$

Pahekotia te x me 8x, ka 9x.

$$16+9x-x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$16+9x-x^{2}-16=0$$

Tangohia te 16 i te 16, ka 0.

$$9x-x^{2}=0$$

Tauwehea te x.

$$x\left(9-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 9-x=0.

$$x=0 x=9$$

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

$$\sqrt{16+0}=0-4$$

Whakarūnātia. Ko te uara x=0 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$4=-4$$

Whakakapia te 9 mō te x i te whārite \sqrt{16+x}=x-4.

$$\sqrt{16+9}=9-4$$

Whakarūnātia. Ko te uara x=9 kua ngata te whārite.

$$5=5$$

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

$$x=9$$