Whakaoti i te 1/2+sqrt{3}+|sin30^circ-1|

$$\frac { 1 } { 2 + \sqrt { 3 } } + | \sin 30 ^ { \circ } - 1 |$$

Aromātai

$$\frac{5}{2}-\sqrt{3}\approx 0.767949192$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{1}{2+\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 2-\sqrt{3}.

$$\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+|\sin(30)-1|$$

Whakaarohia te \left(2+\sqrt{3}\right)\left(2-\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}.

$$\frac{2-\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+|\sin(30)-1|$$

Pūrua 2. Pūrua \sqrt{3}.

$$\frac{2-\sqrt{3}}{4-3}+|\sin(30)-1|$$

Tangohia te 3 i te 4, ka 1.

$$\frac{2-\sqrt{3}}{1}+|\sin(30)-1|$$

Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$2-\sqrt{3}+|\sin(30)-1|$$

Tīkina te uara \sin(30) mai i te ripanga uara pākoki.

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

Tangohia te 1 i te \frac{1}{2}, ka -\frac{1}{2}.

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

Ko te uara pū o tētahi tau tūturu a ko a ina a\geq 0, ko -a rānei ina a<0. Ko te uara pū o -\frac{1}{2} ko \frac{1}{2}.

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

Tāpirihia te 2 ki te \frac{1}{2}, ka \frac{5}{2}.

$$\frac{5}{2}-\sqrt{3}$$