Whakaoti i te x+2=sqrt{2x+7}

$$x + 2 = \sqrt { 2 x + 7 }$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(x+2\right)^{2}=\left(\sqrt{2x+7}\right)^{2}$$

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

$$x^{2}+4x+4=\left(\sqrt{2x+7}\right)^{2}$$

Tātaihia te \sqrt{2x+7} mā te pū o 2, kia riro ko 2x+7.

$$x^{2}+4x+4=2x+7$$

Tangohia te 2x mai i ngā taha e rua.

$$x^{2}+4x+4-2x=7$$

Pahekotia te 4x me -2x, ka 2x.

$$x^{2}+2x+4=7$$

Tangohia te 7 mai i ngā taha e rua.

$$x^{2}+2x+4-7=0$$

Tangohia te 7 i te 4, ka -3.

$$x^{2}+2x-3=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+2x-3 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=3$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

$$\left(x-1\right)\left(x+3\right)$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+3=0.

$$x=1 x=-3$$

Whakakapia te 1 mō te x i te whārite x+2=\sqrt{2x+7}.

$$1+2=\sqrt{2\times 1+7}$$

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

$$3=3$$

Whakakapia te -3 mō te x i te whārite x+2=\sqrt{2x+7}.

$$-3+2=\sqrt{2\left(-3\right)+7}$$

Whakarūnātia. Ko te uara x=-3 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-1=1$$

Ko te whārite x+2=\sqrt{2x+7} he rongoā ahurei.

$$x=1$$