Whakaoti i te sqrt{3x+1}+1=3x

$$\sqrt { 3 x + 1 } + 1 = 3 x$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Me tango 1 mai i ngā taha e rua o te whārite.

$$\sqrt{3x+1}=3x-1$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3x+1}\right)^{2}=\left(3x-1\right)^{2}$$

Tātaihia te \sqrt{3x+1} mā te pū o 2, kia riro ko 3x+1.

$$3x+1=\left(3x-1\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(3x-1\right)^{2}.

$$3x+1=9x^{2}-6x+1$$

Tangohia te 9x^{2} mai i ngā taha e rua.

$$3x+1-9x^{2}=-6x+1$$

Me tāpiri te 6x ki ngā taha e rua.

$$3x+1-9x^{2}+6x=1$$

Pahekotia te 3x me 6x, ka 9x.

$$9x+1-9x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$9x+1-9x^{2}-1=0$$

Tangohia te 1 i te 1, ka 0.

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

Tauwehea te x.

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

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

$$x=0 x=1$$

Whakakapia te 0 mō te x i te whārite \sqrt{3x+1}+1=3x.

$$\sqrt{3\times 0+1}+1=3\times 0$$

Whakarūnātia. Ko te uara x=0 kāore e ngata ana ki te whārite.

$$2=0$$

Whakakapia te 1 mō te x i te whārite \sqrt{3x+1}+1=3x.

$$\sqrt{3\times 1+1}+1=3\times 1$$

Whakarūnātia. Ko te uara x=1 kua ngata te whārite.

$$3=3$$

Ko te whārite \sqrt{3x+1}=3x-1 he rongoā ahurei.

$$x=1$$