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

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

Aromātai

$$2-4\sqrt{3}\approx -4.92820323$$

Ngā Upane Otinga

Whakaarohia te \left(1-2\sqrt{3}\right)\left(2\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}. Pūrua 1.

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

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 4 ki te 3, ka 12.

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

Tangohia te 12 i te 1, ka -11.

$$-11+\left(2\sqrt{3}-1\right)^{2}$$

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

$$-11+4\left(\sqrt{3}\right)^{2}-4\sqrt{3}+1$$

Ko te pūrua o \sqrt{3} ko 3.

$$-11+4\times 3-4\sqrt{3}+1$$

Whakareatia te 4 ki te 3, ka 12.

$$-11+12-4\sqrt{3}+1$$

Tāpirihia te 12 ki te 1, ka 13.

$$-11+13-4\sqrt{3}$$

Tāpirihia te -11 ki te 13, ka 2.

$$2-4\sqrt{3}$$