Whakaoti i te sqrt{16x+17}=x+5

$$\sqrt{ 16x+17 } =x+5$$

Whakaoti mō x

$$x=4$$

$$x=2$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{16x+17}\right)^{2}=\left(x+5\right)^{2}$$

Tātaihia te \sqrt{16x+17} mā te pū o 2, kia riro ko 16x+17.

$$16x+17=\left(x+5\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+5\right)^{2}.

$$16x+17=x^{2}+10x+25$$

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

$$16x+17-x^{2}=10x+25$$

Tangohia te 10x mai i ngā taha e rua.

$$16x+17-x^{2}-10x=25$$

Pahekotia te 16x me -10x, ka 6x.

$$6x+17-x^{2}=25$$

Tangohia te 25 mai i ngā taha e rua.

$$6x+17-x^{2}-25=0$$

Tangohia te 25 i te 17, ka -8.

$$6x-8-x^{2}=0$$

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

$$-x^{2}+6x-8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-\left(-8\right)=8$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 8.

$$1,8 2,4$$

Tātaihia te tapeke mō ia takirua.

$$1+8=9 2+4=6$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=4 b=2$$

Tuhia anō te -x^{2}+6x-8 hei \left(-x^{2}+4x\right)+\left(2x-8\right).

$$\left(-x^{2}+4x\right)+\left(2x-8\right)$$

Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.

$$-x\left(x-4\right)+2\left(x-4\right)$$

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-4\right)\left(-x+2\right)$$

Hei kimi otinga whārite, me whakaoti te x-4=0 me te -x+2=0.

$$x=4 x=2$$

Whakakapia te 4 mō te x i te whārite \sqrt{16x+17}=x+5.

$$\sqrt{16\times 4+17}=4+5$$

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$9=9$$

Whakakapia te 2 mō te x i te whārite \sqrt{16x+17}=x+5.

$$\sqrt{16\times 2+17}=2+5$$

Whakarūnātia. Ko te uara x=2 kua ngata te whārite.

$$7=7$$

Rārangihia ngā rongoā katoa o \sqrt{16x+17}=x+5.

$$x=4 x=2$$