Whakaoti i te sqrt{x+5}+2=sqrt{2x+17}

$$\sqrt { x + 5 } + 2 = \sqrt { 2 x + 17 }$$

Whakaoti mō x

$$x=4$$

$$x=-4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

$$\left(\sqrt{x+5}\right)^{2}+4\sqrt{x+5}+4=\left(\sqrt{2x+17}\right)^{2}$$

Tātaihia te \sqrt{x+5} mā te pū o 2, kia riro ko x+5.

$$x+5+4\sqrt{x+5}+4=\left(\sqrt{2x+17}\right)^{2}$$

Tāpirihia te 5 ki te 4, ka 9.

$$x+9+4\sqrt{x+5}=\left(\sqrt{2x+17}\right)^{2}$$

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

$$x+9+4\sqrt{x+5}=2x+17$$

Me tango x+9 mai i ngā taha e rua o te whārite.

$$4\sqrt{x+5}=2x+17-\left(x+9\right)$$

Hei kimi i te tauaro o x+9, kimihia te tauaro o ia taurangi.

$$4\sqrt{x+5}=2x+17-x-9$$

Pahekotia te 2x me -x, ka x.

$$4\sqrt{x+5}=x+17-9$$

Tangohia te 9 i te 17, ka 8.

$$4\sqrt{x+5}=x+8$$

Pūruatia ngā taha e rua o te whārite.

$$\left(4\sqrt{x+5}\right)^{2}=\left(x+8\right)^{2}$$

Whakarohaina te \left(4\sqrt{x+5}\right)^{2}.

$$4^{2}\left(\sqrt{x+5}\right)^{2}=\left(x+8\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16\left(\sqrt{x+5}\right)^{2}=\left(x+8\right)^{2}$$

Tātaihia te \sqrt{x+5} mā te pū o 2, kia riro ko x+5.

$$16\left(x+5\right)=\left(x+8\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 16 ki te x+5.

$$16x+80=\left(x+8\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+8\right)^{2}.

$$16x+80=x^{2}+16x+64$$

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

$$16x+80-x^{2}=16x+64$$

Tangohia te 16x mai i ngā taha e rua.

$$16x+80-x^{2}-16x=64$$

Pahekotia te 16x me -16x, ka 0.

$$80-x^{2}=64$$

Tangohia te 80 mai i ngā taha e rua.

$$-x^{2}=64-80$$

Tangohia te 80 i te 64, ka -16.

$$-x^{2}=-16$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=\frac{-16}{-1}$$

Ka taea te hautanga \frac{-16}{-1} te whakamāmā ki te 16 mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=16$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=4 x=-4$$

Whakakapia te 4 mō te x i te whārite \sqrt{x+5}+2=\sqrt{2x+17}.

$$\sqrt{4+5}+2=\sqrt{2\times 4+17}$$

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

$$5=5$$

Whakakapia te -4 mō te x i te whārite \sqrt{x+5}+2=\sqrt{2x+17}.

$$\sqrt{-4+5}+2=\sqrt{2\left(-4\right)+17}$$

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

$$3=3$$

Rārangihia ngā rongoā katoa o \sqrt{x+5}+2=\sqrt{2x+17}.

$$x=4 x=-4$$