Whakaoti i te sqrt{4-x}+sqrt{9+x}=5

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

Whakaoti mō x

$$x=-5$$

$$x=0$$

Ngā Upane Otinga

Me tango \sqrt{9+x} mai i ngā taha e rua o te whārite.

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

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{4-x} mā te pū o 2, kia riro ko 4-x.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5-\sqrt{9+x}\right)^{2}.

$$4-x=25-10\sqrt{9+x}+\left(\sqrt{9+x}\right)^{2}$$

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

$$4-x=25-10\sqrt{9+x}+9+x$$

Tāpirihia te 25 ki te 9, ka 34.

$$4-x=34-10\sqrt{9+x}+x$$

Me tango 34+x mai i ngā taha e rua o te whārite.

$$4-x-\left(34+x\right)=-10\sqrt{9+x}$$

Hei kimi i te tauaro o 34+x, kimihia te tauaro o ia taurangi.

$$4-x-34-x=-10\sqrt{9+x}$$

Tangohia te 34 i te 4, ka -30.

$$-30-x-x=-10\sqrt{9+x}$$

Pahekotia te -x me -x, ka -2x.

$$-30-2x=-10\sqrt{9+x}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-30-2x\right)^{2}=\left(-10\sqrt{9+x}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-30-2x\right)^{2}.

$$900+120x+4x^{2}=\left(-10\sqrt{9+x}\right)^{2}$$

Whakarohaina te \left(-10\sqrt{9+x}\right)^{2}.

$$900+120x+4x^{2}=\left(-10\right)^{2}\left(\sqrt{9+x}\right)^{2}$$

Tātaihia te -10 mā te pū o 2, kia riro ko 100.

$$900+120x+4x^{2}=100\left(\sqrt{9+x}\right)^{2}$$

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

$$900+120x+4x^{2}=100\left(9+x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 100 ki te 9+x.

$$900+120x+4x^{2}=900+100x$$

Tangohia te 900 mai i ngā taha e rua.

$$900+120x+4x^{2}-900=100x$$

Tangohia te 900 i te 900, ka 0.

$$120x+4x^{2}=100x$$

Tangohia te 100x mai i ngā taha e rua.

$$120x+4x^{2}-100x=0$$

Pahekotia te 120x me -100x, ka 20x.

$$20x+4x^{2}=0$$

Tauwehea te x.

$$x\left(20+4x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 20+4x=0.

$$x=0 x=-5$$

Whakakapia te 0 mō te x i te whārite \sqrt{4-x}+\sqrt{9+x}=5.

$$\sqrt{4-0}+\sqrt{9+0}=5$$

Whakarūnātia. Ko te uara x=0 kua ngata te whārite.

$$5=5$$

Whakakapia te -5 mō te x i te whārite \sqrt{4-x}+\sqrt{9+x}=5.

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

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

$$5=5$$

Rārangihia ngā rongoā katoa o \sqrt{4-x}=-\sqrt{x+9}+5.

$$x=0 x=-5$$