Whakaoti i te sqrt{m-1}+5=m-2

$$\sqrt { m - 1 } + 5 = m - 2$$

Whakaoti mō m

$$m=10$$

Ngā Upane Otinga

Me tango 5 mai i ngā taha e rua o te whārite.

$$\sqrt{m-1}=m-2-5$$

Tangohia te 5 i te -2, ka -7.

$$\sqrt{m-1}=m-7$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{m-1}\right)^{2}=\left(m-7\right)^{2}$$

Tātaihia te \sqrt{m-1} mā te pū o 2, kia riro ko m-1.

$$m-1=\left(m-7\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(m-7\right)^{2}.

$$m-1=m^{2}-14m+49$$

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

$$m-1-m^{2}=-14m+49$$

Me tāpiri te 14m ki ngā taha e rua.

$$m-1-m^{2}+14m=49$$

Pahekotia te m me 14m, ka 15m.

$$15m-1-m^{2}=49$$

Tangohia te 49 mai i ngā taha e rua.

$$15m-1-m^{2}-49=0$$

Tangohia te 49 i te -1, ka -50.

$$15m-50-m^{2}=0$$

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

$$-m^{2}+15m-50=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -m^{2}+am+bm-50. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=15 ab=-\left(-50\right)=50$$

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 50.

$$1,50 2,25 5,10$$

Tātaihia te tapeke mō ia takirua.

$$1+50=51 2+25=27 5+10=15$$

Ko te otinga te takirua ka hoatu i te tapeke 15.

$$a=10 b=5$$

Tuhia anō te -m^{2}+15m-50 hei \left(-m^{2}+10m\right)+\left(5m-50\right).

$$\left(-m^{2}+10m\right)+\left(5m-50\right)$$

Tauwehea te -m i te tuatahi me te 5 i te rōpū tuarua.

$$-m\left(m-10\right)+5\left(m-10\right)$$

Whakatauwehea atu te kīanga pātahi m-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-10\right)\left(-m+5\right)$$

Hei kimi otinga whārite, me whakaoti te m-10=0 me te -m+5=0.

$$m=10 m=5$$

Whakakapia te 10 mō te m i te whārite \sqrt{m-1}+5=m-2.

$$\sqrt{10-1}+5=10-2$$

Whakarūnātia. Ko te uara m=10 kua ngata te whārite.

$$8=8$$

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

$$\sqrt{5-1}+5=5-2$$

Whakarūnātia. Ko te uara m=5 kāore e ngata ana ki te whārite.

$$7=3$$

Ko te whārite \sqrt{m-1}=m-7 he rongoā ahurei.

$$m=10$$