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

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

Whakaoti mō x

$$x=50\left(\sqrt{3}+1\right)\approx 136.602540378$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

Whakaarohia te \left(\sqrt{3}-1\right)\left(\sqrt{3}+1\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}.

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

Pūrua \sqrt{3}. Pūrua 1.

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

Tangohia te 1 i te 3, ka 2.

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

Whakawehea te 100\left(\sqrt{3}+1\right) ki te 2, kia riro ko 50\left(\sqrt{3}+1\right).

$$50\left(\sqrt{3}+1\right)=x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 50 ki te \sqrt{3}+1.

$$50\sqrt{3}+50=x$$

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

$$x=50\sqrt{3}+50$$