Whakaoti i te frac{100sqrt{3}}{1-sqrt{3}}=x

$$\frac{ 100 \sqrt{ 3 } }{ 1- \sqrt{ 3 } } =x$$

Whakaoti mō x

$$x=-50\sqrt{3}-150\approx -236.602540378$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakangāwaritia te tauraro o \frac{100\sqrt{3}}{1-\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 1+\sqrt{3}.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)}=x$$

Whakaarohia te \left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{1^{2}-\left(\sqrt{3}\right)^{2}}=x$$

Pūrua 1. Pūrua \sqrt{3}.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{1-3}=x$$

Tangohia te 3 i te 1, ka -2.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{-2}=x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 100\sqrt{3} ki te 1+\sqrt{3}.

$$\frac{100\sqrt{3}+100\left(\sqrt{3}\right)^{2}}{-2}=x$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{100\sqrt{3}+100\times 3}{-2}=x$$

Whakareatia te 100 ki te 3, ka 300.

$$\frac{100\sqrt{3}+300}{-2}=x$$

Whakawehea ia wā o 100\sqrt{3}+300 ki te -2, kia riro ko -50\sqrt{3}-150.

$$-50\sqrt{3}-150=x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x=-50\sqrt{3}-150$$