Whakaoti i te (2sqrt{3}-1)^2-(sqrt{3}+2)^2

$$( 2 \sqrt { 3 } - 1 ) ^ { 2 } - ( \sqrt { 3 } + 2 ) ^ { 2 }$$

Aromātai

$$6-8\sqrt{3}\approx -7.856406461$$

Ngā Upane Otinga

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

$$4\left(\sqrt{3}\right)^{2}-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\times 3-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Whakareatia te 4 ki te 3, ka 12.

$$12-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Tāpirihia te 12 ki te 1, ka 13.

$$13-4\sqrt{3}-\left(\sqrt{3}+2\right)^{2}$$

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

$$13-4\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$13-4\sqrt{3}-\left(3+4\sqrt{3}+4\right)$$

Tāpirihia te 3 ki te 4, ka 7.

$$13-4\sqrt{3}-\left(7+4\sqrt{3}\right)$$

Hei kimi i te tauaro o 7+4\sqrt{3}, kimihia te tauaro o ia taurangi.

$$13-4\sqrt{3}-7-4\sqrt{3}$$

Tangohia te 7 i te 13, ka 6.

$$6-4\sqrt{3}-4\sqrt{3}$$

Pahekotia te -4\sqrt{3} me -4\sqrt{3}, ka -8\sqrt{3}.

$$6-8\sqrt{3}$$

Whakaroha

$$6-8\sqrt{3}$$

Ngā Upane Otinga

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

$$4\left(\sqrt{3}\right)^{2}-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$4\times 3-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Whakareatia te 4 ki te 3, ka 12.

$$12-4\sqrt{3}+1-\left(\sqrt{3}+2\right)^{2}$$

Tāpirihia te 12 ki te 1, ka 13.

$$13-4\sqrt{3}-\left(\sqrt{3}+2\right)^{2}$$

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

$$13-4\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4\right)$$

Ko te pūrua o \sqrt{3} ko 3.

$$13-4\sqrt{3}-\left(3+4\sqrt{3}+4\right)$$

Tāpirihia te 3 ki te 4, ka 7.

$$13-4\sqrt{3}-\left(7+4\sqrt{3}\right)$$

Hei kimi i te tauaro o 7+4\sqrt{3}, kimihia te tauaro o ia taurangi.

$$13-4\sqrt{3}-7-4\sqrt{3}$$

Tangohia te 7 i te 13, ka 6.

$$6-4\sqrt{3}-4\sqrt{3}$$

Pahekotia te -4\sqrt{3} me -4\sqrt{3}, ka -8\sqrt{3}.

$$6-8\sqrt{3}$$