Whakaoti i te sqrt{7x+46}-4=x

$$\sqrt { 7 x + 46 } - 4 = x$$

Whakaoti mō x

$$x=5$$

Ngā Upane Otinga

Me tango -4 mai i ngā taha e rua o te whārite.

$$\sqrt{7x+46}=x+4$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{7x+46}\right)^{2}=\left(x+4\right)^{2}$$

Tātaihia te \sqrt{7x+46} mā te pū o 2, kia riro ko 7x+46.

$$7x+46=\left(x+4\right)^{2}$$

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

$$7x+46=x^{2}+8x+16$$

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

$$7x+46-x^{2}=8x+16$$

Tangohia te 8x mai i ngā taha e rua.

$$7x+46-x^{2}-8x=16$$

Pahekotia te 7x me -8x, ka -x.

$$-x+46-x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$-x+46-x^{2}-16=0$$

Tangohia te 16 i te 46, ka 30.

$$-x+30-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}-x+30=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=-30=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$1,-30 2,-15 3,-10 5,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -1.

$$a=5 b=-6$$

Tuhia anō te -x^{2}-x+30 hei \left(-x^{2}+5x\right)+\left(-6x+30\right).

$$\left(-x^{2}+5x\right)+\left(-6x+30\right)$$

Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.

$$x\left(-x+5\right)+6\left(-x+5\right)$$

Whakatauwehea atu te kīanga pātahi -x+5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+5\right)\left(x+6\right)$$

Hei kimi otinga whārite, me whakaoti te -x+5=0 me te x+6=0.

$$x=5 x=-6$$

Whakakapia te 5 mō te x i te whārite \sqrt{7x+46}-4=x.

$$\sqrt{7\times 5+46}-4=5$$

Whakarūnātia. Ko te uara x=5 kua ngata te whārite.

$$5=5$$

Whakakapia te -6 mō te x i te whārite \sqrt{7x+46}-4=x.

$$\sqrt{7\left(-6\right)+46}-4=-6$$

Whakarūnātia. Ko te uara x=-6 kāore e ngata ana ki te whārite.

$$-2=-6$$

Ko te whārite \sqrt{7x+46}=x+4 he rongoā ahurei.

$$x=5$$