Whakaoti i te sqrt{2a-3}+3=a

$$\sqrt { 2 a - 3 } + 3 = a$$

Whakaoti mō a

$$a=6$$

Ngā Upane Otinga

Me tango 3 mai i ngā taha e rua o te whārite.

$$\sqrt{2a-3}=a-3$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2a-3}\right)^{2}=\left(a-3\right)^{2}$$

Tātaihia te \sqrt{2a-3} mā te pū o 2, kia riro ko 2a-3.

$$2a-3=\left(a-3\right)^{2}$$

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

$$2a-3=a^{2}-6a+9$$

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

$$2a-3-a^{2}=-6a+9$$

Me tāpiri te 6a ki ngā taha e rua.

$$2a-3-a^{2}+6a=9$$

Pahekotia te 2a me 6a, ka 8a.

$$8a-3-a^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$8a-3-a^{2}-9=0$$

Tangohia te 9 i te -3, ka -12.

$$8a-12-a^{2}=0$$

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

$$-a^{2}+8a-12=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -a^{2}+aa+ba-12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-\left(-12\right)=12$$

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 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=6 b=2$$

Tuhia anō te -a^{2}+8a-12 hei \left(-a^{2}+6a\right)+\left(2a-12\right).

$$\left(-a^{2}+6a\right)+\left(2a-12\right)$$

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

$$-a\left(a-6\right)+2\left(a-6\right)$$

Whakatauwehea atu te kīanga pātahi a-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-6\right)\left(-a+2\right)$$

Hei kimi otinga whārite, me whakaoti te a-6=0 me te -a+2=0.

$$a=6 a=2$$

Whakakapia te 6 mō te a i te whārite \sqrt{2a-3}+3=a.

$$\sqrt{2\times 6-3}+3=6$$

Whakarūnātia. Ko te uara a=6 kua ngata te whārite.

$$6=6$$

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

$$\sqrt{2\times 2-3}+3=2$$

Whakarūnātia. Ko te uara a=2 kāore e ngata ana ki te whārite.

$$4=2$$

Ko te whārite \sqrt{2a-3}=a-3 he rongoā ahurei.

$$a=6$$