Datrys (frac{-1-sqrt{5}}{2})^2

$$( \frac { - 1 - \sqrt { 5 } } { 2 } ) ^ { 2 }$$

Enrhifo

$$\frac{\sqrt{5}+3}{2}\approx 2.618033989$$

Camau Ateb

I godi \frac{-1-\sqrt{5}}{2} i bŵer, codwch y rhifiadur a'r enwadur i bŵer ac yna rhannwch nhw.

$$\frac{\left(-1-\sqrt{5}\right)^{2}}{2^{2}}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(-1-\sqrt{5}\right)^{2}.

$$\frac{1+2\sqrt{5}+\left(\sqrt{5}\right)^{2}}{2^{2}}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{1+2\sqrt{5}+5}{2^{2}}$$

Adio 1 a 5 i gael 6.

$$\frac{6+2\sqrt{5}}{2^{2}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

$$\frac{6+2\sqrt{5}}{4}$$

Ehangu

$$\frac{\sqrt{5} + 3}{2} = 2.618033988749895$$

Camau Ateb

I godi \frac{-1-\sqrt{5}}{2} i bŵer, codwch y rhifiadur a'r enwadur i bŵer ac yna rhannwch nhw.

$$\frac{\left(-1-\sqrt{5}\right)^{2}}{2^{2}}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(-1-\sqrt{5}\right)^{2}.

$$\frac{1+2\sqrt{5}+\left(\sqrt{5}\right)^{2}}{2^{2}}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{1+2\sqrt{5}+5}{2^{2}}$$

Adio 1 a 5 i gael 6.

$$\frac{6+2\sqrt{5}}{2^{2}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

$$\frac{6+2\sqrt{5}}{4}$$