Whakaoti i te sqrt{5x+12}=x+3

$$\sqrt{ 5x+12 } =x+3$$

Whakaoti mō x

$$x = \frac{\sqrt{13} - 1}{2} \approx 1.302775638$$

$$x=\frac{-\sqrt{13}-1}{2}\approx -2.302775638$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{5x+12}\right)^{2}=\left(x+3\right)^{2}$$

Tātaihia te \sqrt{5x+12} mā te pū o 2, kia riro ko 5x+12.

$$5x+12=\left(x+3\right)^{2}$$

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

$$5x+12=x^{2}+6x+9$$

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

$$5x+12-x^{2}=6x+9$$

Tangohia te 6x mai i ngā taha e rua.

$$5x+12-x^{2}-6x=9$$

Pahekotia te 5x me -6x, ka -x.

$$-x+12-x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$-x+12-x^{2}-9=0$$

Tangohia te 9 i te 12, ka 3.

$$-x+3-x^{2}=0$$

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.

$$-x^{2}-x+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -1 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-1\right)±\sqrt{1+4\times 3}}{2\left(-1\right)}$$

Whakareatia 4 ki te 3.

$$x=\frac{-\left(-1\right)±\sqrt{1+12}}{2\left(-1\right)}$$

Tāpiri 1 ki te 12.

$$x=\frac{-\left(-1\right)±\sqrt{13}}{2\left(-1\right)}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{13}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{1±\sqrt{13}}{-2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{13}}{-2} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{13}.

$$x=\frac{\sqrt{13}+1}{-2}$$

Whakawehe 1+\sqrt{13} ki te -2.

$$x=\frac{-\sqrt{13}-1}{2}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{13}}{-2} ina he tango te ±. Tango \sqrt{13} mai i 1.

$$x=\frac{1-\sqrt{13}}{-2}$$

Whakawehe 1-\sqrt{13} ki te -2.

$$x=\frac{\sqrt{13}-1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{13}-1}{2} x=\frac{\sqrt{13}-1}{2}$$

Whakakapia te \frac{-\sqrt{13}-1}{2} mō te x i te whārite \sqrt{5x+12}=x+3.

$$\sqrt{5\times \frac{-\sqrt{13}-1}{2}+12}=\frac{-\sqrt{13}-1}{2}+3$$

Whakarūnātia. Ko te uara x=\frac{-\sqrt{13}-1}{2} kua ngata te whārite.

$$\frac{5}{2}-\frac{1}{2}\times 13^{\frac{1}{2}}=-\frac{1}{2}\times 13^{\frac{1}{2}}+\frac{5}{2}$$

Whakakapia te \frac{\sqrt{13}-1}{2} mō te x i te whārite \sqrt{5x+12}=x+3.

$$\sqrt{5\times \frac{\sqrt{13}-1}{2}+12}=\frac{\sqrt{13}-1}{2}+3$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{13}-1}{2} kua ngata te whārite.

$$\frac{5}{2}+\frac{1}{2}\times 13^{\frac{1}{2}}=\frac{1}{2}\times 13^{\frac{1}{2}}+\frac{5}{2}$$

Rārangihia ngā rongoā katoa o \sqrt{5x+12}=x+3.

$$x=\frac{-\sqrt{13}-1}{2} x=\frac{\sqrt{13}-1}{2}$$