Datrys (frac{sqrt{5}+1}{4})^2

$$( \frac { \sqrt { 5 } + 1 } { 4 } ) ^ { 2 }$$

Enrhifo

$$\frac{\sqrt{5}+3}{8}\approx 0.654508497$$

Camau Ateb

I godi \frac{\sqrt{5}+1}{4} i bŵer, codwch y rhifiadur a'r enwadur i bŵer ac yna rhannwch nhw.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{4^{2}}$$

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

$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}+1}{4^{2}}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{5+2\sqrt{5}+1}{4^{2}}$$

Adio 5 a 1 i gael 6.

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

Cyfrifo 4 i bŵer 2 a chael 16.

$$\frac{6+2\sqrt{5}}{16}$$

Ehangu

$$\frac{\sqrt{5} + 3}{8} = 0.6545084971874737$$

Camau Ateb

I godi \frac{\sqrt{5}+1}{4} i bŵer, codwch y rhifiadur a'r enwadur i bŵer ac yna rhannwch nhw.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{4^{2}}$$

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

$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}+1}{4^{2}}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{5+2\sqrt{5}+1}{4^{2}}$$

Adio 5 a 1 i gael 6.

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

Cyfrifo 4 i bŵer 2 a chael 16.

$$\frac{6+2\sqrt{5}}{16}$$