Whakaoti i te 2sqrt{9x}-6=10-2sqrt{x}

$$2 \sqrt { 9 x } - 6 = 10 - 2 \sqrt { x }$$

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

Me tango -6 mai i ngā taha e rua o te whārite.

$$2\sqrt{9x}=10-2\sqrt{x}+6$$

Pūruatia ngā taha e rua o te whārite.

$$\left(2\sqrt{9x}\right)^{2}=\left(10-2\sqrt{x}+6\right)^{2}$$

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

$$2^{2}\left(\sqrt{9x}\right)^{2}=\left(10-2\sqrt{x}+6\right)^{2}$$

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

$$4\left(\sqrt{9x}\right)^{2}=\left(10-2\sqrt{x}+6\right)^{2}$$

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

$$4\times 9x=\left(10-2\sqrt{x}+6\right)^{2}$$

Whakareatia te 4 ki te 9, ka 36.

$$36x=\left(10-2\sqrt{x}+6\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(10-2\sqrt{x}+6\right)^{2}.

$$36x=\left(10-2\sqrt{x}\right)^{2}+12\left(10-2\sqrt{x}\right)+36$$

Tangohia te \left(10-2\sqrt{x}\right)^{2} mai i ngā taha e rua.

$$36x-\left(10-2\sqrt{x}\right)^{2}=12\left(10-2\sqrt{x}\right)+36$$

Tangohia te 12\left(10-2\sqrt{x}\right) mai i ngā taha e rua.

$$36x-\left(10-2\sqrt{x}\right)^{2}-12\left(10-2\sqrt{x}\right)=36$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(10-2\sqrt{x}\right)^{2}.

$$36x-\left(100-40\sqrt{x}+4\left(\sqrt{x}\right)^{2}\right)-12\left(10-2\sqrt{x}\right)=36$$

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

$$36x-\left(100-40\sqrt{x}+4x\right)-12\left(10-2\sqrt{x}\right)=36$$

Hei kimi i te tauaro o 100-40\sqrt{x}+4x, kimihia te tauaro o ia taurangi.

$$36x-100+40\sqrt{x}-4x-12\left(10-2\sqrt{x}\right)=36$$

Pahekotia te 36x me -4x, ka 32x.

$$32x-100+40\sqrt{x}-12\left(10-2\sqrt{x}\right)=36$$

Whakamahia te āhuatanga tohatoha hei whakarea te -12 ki te 10-2\sqrt{x}.

$$32x-100+40\sqrt{x}-120+24\sqrt{x}=36$$

Tangohia te 120 i te -100, ka -220.

$$32x-220+40\sqrt{x}+24\sqrt{x}=36$$

Pahekotia te 40\sqrt{x} me 24\sqrt{x}, ka 64\sqrt{x}.

$$32x-220+64\sqrt{x}=36$$

Me tāpiri te 220 ki ngā taha e rua.

$$32x+64\sqrt{x}=36+220$$

Tāpirihia te 36 ki te 220, ka 256.

$$32x+64\sqrt{x}=256$$

Me tango 32x mai i ngā taha e rua o te whārite.

$$64\sqrt{x}=256-32x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(64\sqrt{x}\right)^{2}=\left(-32x+256\right)^{2}$$

Whakarohaina te \left(64\sqrt{x}\right)^{2}.

$$64^{2}\left(\sqrt{x}\right)^{2}=\left(-32x+256\right)^{2}$$

Tātaihia te 64 mā te pū o 2, kia riro ko 4096.

$$4096\left(\sqrt{x}\right)^{2}=\left(-32x+256\right)^{2}$$

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

$$4096x=\left(-32x+256\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-32x+256\right)^{2}.

$$4096x=1024x^{2}-16384x+65536$$

Tangohia te 1024x^{2} mai i ngā taha e rua.

$$4096x-1024x^{2}=-16384x+65536$$

Me tāpiri te 16384x ki ngā taha e rua.

$$4096x-1024x^{2}+16384x=65536$$

Pahekotia te 4096x me 16384x, ka 20480x.

$$20480x-1024x^{2}=65536$$

Tangohia te 65536 mai i ngā taha e rua.

$$20480x-1024x^{2}-65536=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-1024x^{2}+20480x-65536=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1024 mō a, 20480 mō b, me -65536 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20480±\sqrt{20480^{2}-4\left(-1024\right)\left(-65536\right)}}{2\left(-1024\right)}$$

Pūrua 20480.

$$x=\frac{-20480±\sqrt{419430400-4\left(-1024\right)\left(-65536\right)}}{2\left(-1024\right)}$$

Whakareatia -4 ki te -1024.

$$x=\frac{-20480±\sqrt{419430400+4096\left(-65536\right)}}{2\left(-1024\right)}$$

Whakareatia 4096 ki te -65536.

$$x=\frac{-20480±\sqrt{419430400-268435456}}{2\left(-1024\right)}$$

Tāpiri 419430400 ki te -268435456.

$$x=\frac{-20480±\sqrt{150994944}}{2\left(-1024\right)}$$

Tuhia te pūtakerua o te 150994944.

$$x=\frac{-20480±12288}{2\left(-1024\right)}$$

Whakareatia 2 ki te -1024.

$$x=\frac{-20480±12288}{-2048}$$

Nā, me whakaoti te whārite x=\frac{-20480±12288}{-2048} ina he tāpiri te ±. Tāpiri -20480 ki te 12288.

$$x=-\frac{8192}{-2048}$$

Whakawehe -8192 ki te -2048.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-20480±12288}{-2048} ina he tango te ±. Tango 12288 mai i -20480.

$$x=-\frac{32768}{-2048}$$

Whakawehe -32768 ki te -2048.

$$x=16$$

Kua oti te whārite te whakatau.

$$x=4 x=16$$

Whakakapia te 4 mō te x i te whārite 2\sqrt{9x}-6=10-2\sqrt{x}.

$$2\sqrt{9\times 4}-6=10-2\sqrt{4}$$

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

$$6=6$$

Whakakapia te 16 mō te x i te whārite 2\sqrt{9x}-6=10-2\sqrt{x}.

$$2\sqrt{9\times 16}-6=10-2\sqrt{16}$$

Whakarūnātia. Ko te uara x=16 kāore e ngata ana ki te whārite.

$$18=2$$

Whakakapia te 4 mō te x i te whārite 2\sqrt{9x}-6=10-2\sqrt{x}.

$$2\sqrt{9\times 4}-6=10-2\sqrt{4}$$

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

$$6=6$$

Ko te whārite 2\sqrt{9x}=10-2\sqrt{x}+6 he rongoā ahurei.

$$x=4$$