Whakaoti i te (frac{2sqrt{3}x}{3})^2=x(sqrt{7}-x)

$$( \frac { 2 \sqrt { 3 } x } { 3 } ) ^ { 2 } = x ( \sqrt { 7 } - x )$$

Whakaoti mō x

$$x = \frac{3 \sqrt{7}}{7} \approx 1.133893419$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Kia whakarewa i te \frac{2\sqrt{3}x}{3} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(2\sqrt{3}x\right)^{2}}{3^{2}}=x\left(\sqrt{7}-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te \sqrt{7}-x.

$$\frac{\left(2\sqrt{3}x\right)^{2}}{3^{2}}=x\sqrt{7}-x^{2}$$

Whakarohaina te \left(2\sqrt{3}x\right)^{2}.

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}x^{2}}{3^{2}}=x\sqrt{7}-x^{2}$$

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

$$\frac{4\left(\sqrt{3}\right)^{2}x^{2}}{3^{2}}=x\sqrt{7}-x^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4\times 3x^{2}}{3^{2}}=x\sqrt{7}-x^{2}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{12x^{2}}{3^{2}}=x\sqrt{7}-x^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{12x^{2}}{9}=x\sqrt{7}-x^{2}$$

Whakawehea te 12x^{2} ki te 9, kia riro ko \frac{4}{3}x^{2}.

$$\frac{4}{3}x^{2}=x\sqrt{7}-x^{2}$$

Tangohia te x\sqrt{7} mai i ngā taha e rua.

$$\frac{4}{3}x^{2}-x\sqrt{7}=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{4}{3}x^{2}-x\sqrt{7}+x^{2}=0$$

Pahekotia te \frac{4}{3}x^{2} me x^{2}, ka \frac{7}{3}x^{2}.

$$\frac{7}{3}x^{2}-x\sqrt{7}=0$$

Tauwehea te x.

$$x\left(\frac{7}{3}x-\sqrt{7}\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{7x}{3}-\sqrt{7}=0.

$$x=0 x=\frac{3\sqrt{7}}{7}$$