Whakaoti i te sqrt{15-x}-sqrt{6x}=-3

$$\sqrt{ 15-x } - \sqrt{ 6x } =-3$$

Whakaoti mō x

$$x=6$$

Ngā Upane Otinga

Me tango -\sqrt{6x} mai i ngā taha e rua o te whārite.

$$\sqrt{15-x}=-3+\sqrt{6x}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{15-x}\right)^{2}=\left(-3+\sqrt{6x}\right)^{2}$$

Tātaihia te \sqrt{15-x} mā te pū o 2, kia riro ko 15-x.

$$15-x=\left(-3+\sqrt{6x}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-3+\sqrt{6x}\right)^{2}.

$$15-x=9-6\sqrt{6x}+\left(\sqrt{6x}\right)^{2}$$

Tātaihia te \sqrt{6x} mā te pū o 2, kia riro ko 6x.

$$15-x=9-6\sqrt{6x}+6x$$

Me tango 9+6x mai i ngā taha e rua o te whārite.

$$15-x-\left(9+6x\right)=-6\sqrt{6x}$$

Hei kimi i te tauaro o 9+6x, kimihia te tauaro o ia taurangi.

$$15-x-9-6x=-6\sqrt{6x}$$

Tangohia te 9 i te 15, ka 6.

$$6-x-6x=-6\sqrt{6x}$$

Pahekotia te -x me -6x, ka -7x.

$$6-7x=-6\sqrt{6x}$$

Pūruatia ngā taha e rua o te whārite.

$$\left(6-7x\right)^{2}=\left(-6\sqrt{6x}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(6-7x\right)^{2}.

$$36-84x+49x^{2}=\left(-6\sqrt{6x}\right)^{2}$$

Whakarohaina te \left(-6\sqrt{6x}\right)^{2}.

$$36-84x+49x^{2}=\left(-6\right)^{2}\left(\sqrt{6x}\right)^{2}$$

Tātaihia te -6 mā te pū o 2, kia riro ko 36.

$$36-84x+49x^{2}=36\left(\sqrt{6x}\right)^{2}$$

Tātaihia te \sqrt{6x} mā te pū o 2, kia riro ko 6x.

$$36-84x+49x^{2}=36\times 6x$$

Whakareatia te 36 ki te 6, ka 216.

$$36-84x+49x^{2}=216x$$

Tangohia te 216x mai i ngā taha e rua.

$$36-84x+49x^{2}-216x=0$$

Pahekotia te -84x me -216x, ka -300x.

$$36-300x+49x^{2}=0$$

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.

$$49x^{2}-300x+36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 49 mō a, -300 mō b, me 36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-300\right)±\sqrt{\left(-300\right)^{2}-4\times 49\times 36}}{2\times 49}$$

Pūrua -300.

$$x=\frac{-\left(-300\right)±\sqrt{90000-4\times 49\times 36}}{2\times 49}$$

Whakareatia -4 ki te 49.

$$x=\frac{-\left(-300\right)±\sqrt{90000-196\times 36}}{2\times 49}$$

Whakareatia -196 ki te 36.

$$x=\frac{-\left(-300\right)±\sqrt{90000-7056}}{2\times 49}$$

Tāpiri 90000 ki te -7056.

$$x=\frac{-\left(-300\right)±\sqrt{82944}}{2\times 49}$$

Tuhia te pūtakerua o te 82944.

$$x=\frac{-\left(-300\right)±288}{2\times 49}$$

Ko te tauaro o -300 ko 300.

$$x=\frac{300±288}{2\times 49}$$

Whakareatia 2 ki te 49.

$$x=\frac{300±288}{98}$$

Nā, me whakaoti te whārite x=\frac{300±288}{98} ina he tāpiri te ±. Tāpiri 300 ki te 288.

$$x=\frac{588}{98}$$

Whakawehe 588 ki te 98.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{300±288}{98} ina he tango te ±. Tango 288 mai i 300.

$$x=\frac{12}{98}$$

Whakahekea te hautanga \frac{12}{98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{6}{49}$$

Kua oti te whārite te whakatau.

$$x=6 x=\frac{6}{49}$$

Whakakapia te 6 mō te x i te whārite \sqrt{15-x}-\sqrt{6x}=-3.

$$\sqrt{15-6}-\sqrt{6\times 6}=-3$$

Whakarūnātia. Ko te uara x=6 kua ngata te whārite.

$$-3=-3$$

Whakakapia te \frac{6}{49} mō te x i te whārite \sqrt{15-x}-\sqrt{6x}=-3.

$$\sqrt{15-\frac{6}{49}}-\sqrt{6\times \frac{6}{49}}=-3$$

Whakarūnātia. Ko te uara x=\frac{6}{49} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$3=-3$$

Whakakapia te 6 mō te x i te whārite \sqrt{15-x}-\sqrt{6x}=-3.

$$\sqrt{15-6}-\sqrt{6\times 6}=-3$$

Whakarūnātia. Ko te uara x=6 kua ngata te whārite.

$$-3=-3$$

Ko te whārite \sqrt{15-x}=\sqrt{6x}-3 he rongoā ahurei.

$$x=6$$