Whakaoti i te sqrt{9x-20}=x

$$\sqrt { 9 x - 20 } = x$$

Whakaoti mō x

$$x=5$$

$$x=4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{9x-20}\right)^{2}=x^{2}$$

Tātaihia te \sqrt{9x-20} mā te pū o 2, kia riro ko 9x-20.

$$9x-20=x^{2}$$

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

$$9x-20-x^{2}=0$$

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

$$-x^{2}+9x-20=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=-\left(-20\right)=20$$

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 20.

$$1,20 2,10 4,5$$

Tātaihia te tapeke mō ia takirua.

$$1+20=21 2+10=12 4+5=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=5 b=4$$

Tuhia anō te -x^{2}+9x-20 hei \left(-x^{2}+5x\right)+\left(4x-20\right).

$$\left(-x^{2}+5x\right)+\left(4x-20\right)$$

Tauwehea te -x i te tuatahi me te 4 i te rōpū tuarua.

$$-x\left(x-5\right)+4\left(x-5\right)$$

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

$$\left(x-5\right)\left(-x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x-5=0 me te -x+4=0.

$$x=5 x=4$$

Whakakapia te 5 mō te x i te whārite \sqrt{9x-20}=x.

$$\sqrt{9\times 5-20}=5$$

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

$$5=5$$

Whakakapia te 4 mō te x i te whārite \sqrt{9x-20}=x.

$$\sqrt{9\times 4-20}=4$$

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

$$4=4$$

Rārangihia ngā rongoā katoa o \sqrt{9x-20}=x.

$$x=5 x=4$$