Whakaoti i te {l}{(4-sqrt{3})(4+sqrt{3})}{(1+sqrt{5})^2-sqrt{20}}

$$\left. \begin{array} { l } { ( 4 - \sqrt { 3 } ) ( 4 + \sqrt { 3 } ) } \\ { ( 1 + \sqrt { 5 } ) ^ { 2 } - \sqrt { 20 } } \end{array} \right.$$

Kōmaka

$$6,13$$

Ngā Upane Otinga

Whakaarohia te \left(4-\sqrt{3}\right)\left(4+\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}. Pūrua 4.

$$sort(16-\left(\sqrt{3}\right)^{2},\left(1+\sqrt{5}\right)^{2}-\sqrt{20})$$

Ko te pūrua o \sqrt{3} ko 3.

$$sort(16-3,\left(1+\sqrt{5}\right)^{2}-\sqrt{20})$$

Tangohia te 3 i te 16, ka 13.

$$sort(13,\left(1+\sqrt{5}\right)^{2}-\sqrt{20})$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(1+\sqrt{5}\right)^{2}.

$$sort(13,1+2\sqrt{5}+\left(\sqrt{5}\right)^{2}-\sqrt{20})$$

Ko te pūrua o \sqrt{5} ko 5.

$$sort(13,1+2\sqrt{5}+5-\sqrt{20})$$

Tāpirihia te 1 ki te 5, ka 6.

$$sort(13,6+2\sqrt{5}-\sqrt{20})$$

Tauwehea te 20=2^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 5} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{5}. Tuhia te pūtakerua o te 2^{2}.

$$sort(13,6+2\sqrt{5}-2\sqrt{5})$$

Pahekotia te 2\sqrt{5} me -2\sqrt{5}, ka 0.

$$sort(13,6)$$

Hei kōmaka i te rārangi, me tīmata mai i tētahi huānga 13 kotahi.

$$13$$

Me kōkuhu te 6 ki te tauwāhi tika i te rārangi hōu.

$$6,13$$

Aromātai

$$13,\ 6$$