Datrys (2sqrt{3}-1)^2-(sqrt{3}+2)^2

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

Enrhifo

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

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(2\sqrt{3}-1\right)^{2}.

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

Sgwâr \sqrt{3} yw 3.

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

Lluosi 4 a 3 i gael 12.

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

Adio 12 a 1 i gael 13.

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

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(\sqrt{3}+2\right)^{2}.

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

Sgwâr \sqrt{3} yw 3.

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

Adio 3 a 4 i gael 7.

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

I ddod o hyd i wrthwyneb 7+4\sqrt{3}, dewch o hyd i wrthwyneb pob term.

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

Tynnu 7 o 13 i gael 6.

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

Cyfuno -4\sqrt{3} a -4\sqrt{3} i gael -8\sqrt{3}.

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

Ehangu

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

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(2\sqrt{3}-1\right)^{2}.

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

Sgwâr \sqrt{3} yw 3.

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

Lluosi 4 a 3 i gael 12.

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

Adio 12 a 1 i gael 13.

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

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(\sqrt{3}+2\right)^{2}.

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

Sgwâr \sqrt{3} yw 3.

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

Adio 3 a 4 i gael 7.

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

I ddod o hyd i wrthwyneb 7+4\sqrt{3}, dewch o hyd i wrthwyneb pob term.

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

Tynnu 7 o 13 i gael 6.

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

Cyfuno -4\sqrt{3} a -4\sqrt{3} i gael -8\sqrt{3}.

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