Whakaoti i te 2v=sqrt{5v^2-6v+5}

$$2 v = \sqrt { 5 v ^ { 2 } - 6 v + 5 }$$

Whakaoti mō v

$$v=5$$

$$v=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(2v\right)^{2}=\left(\sqrt{5v^{2}-6v+5}\right)^{2}$$

Whakarohaina te \left(2v\right)^{2}.

$$2^{2}v^{2}=\left(\sqrt{5v^{2}-6v+5}\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4v^{2}=\left(\sqrt{5v^{2}-6v+5}\right)^{2}$$

Tātaihia te \sqrt{5v^{2}-6v+5} mā te pū o 2, kia riro ko 5v^{2}-6v+5.

$$4v^{2}=5v^{2}-6v+5$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$4v^{2}-5v^{2}=-6v+5$$

Pahekotia te 4v^{2} me -5v^{2}, ka -v^{2}.

$$-v^{2}=-6v+5$$

Me tāpiri te 6v ki ngā taha e rua.

$$-v^{2}+6v=5$$

Tangohia te 5 mai i ngā taha e rua.

$$-v^{2}+6v-5=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -v^{2}+av+bv-5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-\left(-5\right)=5$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=5 b=1$$

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

$$\left(-v^{2}+5v\right)+\left(v-5\right)$$

Whakatauwehea atu -v i te -v^{2}+5v.

$$-v\left(v-5\right)+v-5$$

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

$$\left(v-5\right)\left(-v+1\right)$$

Hei kimi otinga whārite, me whakaoti te v-5=0 me te -v+1=0.

$$v=5 v=1$$

Whakakapia te 5 mō te v i te whārite 2v=\sqrt{5v^{2}-6v+5}.

$$2\times 5=\sqrt{5\times 5^{2}-6\times 5+5}$$

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

$$10=10$$

Whakakapia te 1 mō te v i te whārite 2v=\sqrt{5v^{2}-6v+5}.

$$2\times 1=\sqrt{5\times 1^{2}-6+5}$$

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

$$2=2$$

Rārangihia ngā rongoā katoa o 2v=\sqrt{5v^{2}-6v+5}.

$$v=5 v=1$$