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

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

Enrhifo

$$\sqrt{5}\approx 2.236067977$$

Camau Ateb Byr

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

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

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

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

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

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

Sgwâr \sqrt{5} yw 5.

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

Adio 5 a 1 i gael 6.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{2^{2}}-\frac{6-2\sqrt{5}}{2^{2}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{2^{2}}-\frac{6-2\sqrt{5}}{4}$$

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Ehangu 2^{2}.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{4}-\frac{6-2\sqrt{5}}{4}$$

Gan fod gan \frac{\left(\sqrt{5}+1\right)^{2}}{4} a \frac{6-2\sqrt{5}}{4} yr un dynodydd, tynnwch nhw drwy dynnu eu rhifiaduron.

$$\frac{\left(\sqrt{5}+1\right)^{2}-\left(6-2\sqrt{5}\right)}{4}$$

Gwnewch y gwaith lluosi yn \left(\sqrt{5}+1\right)^{2}-\left(6-2\sqrt{5}\right).

$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}+1-6+2\sqrt{5}}{4}$$

Gwnewch y gwaith cyfrifo yn \left(\sqrt{5}\right)^{2}+2\sqrt{5}+1-6+2\sqrt{5}.

$$\frac{4\sqrt{5}}{4}$$

Canslo 4 a 4.

$$\sqrt{5}$$

Ehangu

$$\sqrt{5} = 2.236067977$$

Camau Ateb Byr

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

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

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

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

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

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

Sgwâr \sqrt{5} yw 5.

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

Adio 5 a 1 i gael 6.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{2^{2}}-\frac{6-2\sqrt{5}}{2^{2}}$$

Cyfrifo 2 i bŵer 2 a chael 4.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{2^{2}}-\frac{6-2\sqrt{5}}{4}$$

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Ehangu 2^{2}.

$$\frac{\left(\sqrt{5}+1\right)^{2}}{4}-\frac{6-2\sqrt{5}}{4}$$

Gan fod gan \frac{\left(\sqrt{5}+1\right)^{2}}{4} a \frac{6-2\sqrt{5}}{4} yr un dynodydd, tynnwch nhw drwy dynnu eu rhifiaduron.

$$\frac{\left(\sqrt{5}+1\right)^{2}-\left(6-2\sqrt{5}\right)}{4}$$

Gwnewch y gwaith lluosi yn \left(\sqrt{5}+1\right)^{2}-\left(6-2\sqrt{5}\right).

$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}+1-6+2\sqrt{5}}{4}$$

Gwnewch y gwaith cyfrifo yn \left(\sqrt{5}\right)^{2}+2\sqrt{5}+1-6+2\sqrt{5}.

$$\frac{4\sqrt{5}}{4}$$

Canslo 4 a 4.

$$\sqrt{5}$$