Whakaoti i te frac{sqrt{3}-1}{sqrt{3}+1}*frac{sqrt{3}+1}{sqrt{3}+1}

$$\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \times \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } + 1 }$$

Aromātai

$$2-\sqrt{3}\approx 0.267949192$$

Ngā Upane Otinga

Whakawehea te \sqrt{3}+1 ki te \sqrt{3}+1, kia riro ko 1.

$$\frac{\sqrt{3}-1}{\sqrt{3}+1}\times 1$$

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

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\times 1$$

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}.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}\times 1$$

Pūrua \sqrt{3}. Pūrua 1.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{3-1}\times 1$$

Tangohia te 1 i te 3, ka 2.

$$\frac{\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)}{2}\times 1$$

Whakareatia te \sqrt{3}-1 ki te \sqrt{3}-1, ka \left(\sqrt{3}-1\right)^{2}.

$$\frac{\left(\sqrt{3}-1\right)^{2}}{2}\times 1$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\sqrt{3}-1\right)^{2}.

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

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{3-2\sqrt{3}+1}{2}\times 1$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{4-2\sqrt{3}}{2}\times 1$$

Whakawehea ia wā o 4-2\sqrt{3} ki te 2, kia riro ko 2-\sqrt{3}.

$$\left(2-\sqrt{3}\right)\times 1$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2-\sqrt{3} ki te 1.

$$2-\sqrt{3}$$

Tauwehe

$$2-\sqrt{3}$$