Datrys frac{8+4-2sqrt{5}-4sqrt{5}+2sqrt{10}}{1-sqrt{5}}

$$\frac { 8 + 4 - 2 \sqrt { 5 } - 4 \sqrt { 5 } + 2 \sqrt { 10 } } { 1 - \sqrt { 5 } }$$

Enrhifo

$$\frac{9-\sqrt{10}-3\sqrt{5}-5\sqrt{2}}{2}\approx -3.970774702$$

Camau Ateb

Adio 8 a 4 i gael 12.

$$\frac{12-2\sqrt{5}-4\sqrt{5}+2\sqrt{10}}{1-\sqrt{5}}$$

Cyfuno -2\sqrt{5} a -4\sqrt{5} i gael -6\sqrt{5}.

$$\frac{12-6\sqrt{5}+2\sqrt{10}}{1-\sqrt{5}}$$

Mae'n rhesymoli enwadur \frac{12-6\sqrt{5}+2\sqrt{10}}{1-\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â 1+\sqrt{5}.

$$\frac{\left(12-6\sqrt{5}+2\sqrt{10}\right)\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}$$

Ystyriwch \left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(12-6\sqrt{5}+2\sqrt{10}\right)\left(1+\sqrt{5}\right)}{1^{2}-\left(\sqrt{5}\right)^{2}}$$

Sgwâr 1. Sgwâr \sqrt{5}.

$$\frac{\left(12-6\sqrt{5}+2\sqrt{10}\right)\left(1+\sqrt{5}\right)}{1-5}$$

Tynnu 5 o 1 i gael -4.

$$\frac{\left(12-6\sqrt{5}+2\sqrt{10}\right)\left(1+\sqrt{5}\right)}{-4}$$

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 12-6\sqrt{5}+2\sqrt{10} gan bob 1+\sqrt{5}.

$$\frac{12+12\sqrt{5}-6\sqrt{5}-6\left(\sqrt{5}\right)^{2}+2\sqrt{10}+2\sqrt{10}\sqrt{5}}{-4}$$

Cyfuno 12\sqrt{5} a -6\sqrt{5} i gael 6\sqrt{5}.

$$\frac{12+6\sqrt{5}-6\left(\sqrt{5}\right)^{2}+2\sqrt{10}+2\sqrt{10}\sqrt{5}}{-4}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{12+6\sqrt{5}-6\times 5+2\sqrt{10}+2\sqrt{10}\sqrt{5}}{-4}$$

Lluosi -6 a 5 i gael -30.

$$\frac{12+6\sqrt{5}-30+2\sqrt{10}+2\sqrt{10}\sqrt{5}}{-4}$$

Tynnu 30 o 12 i gael -18.

$$\frac{-18+6\sqrt{5}+2\sqrt{10}+2\sqrt{10}\sqrt{5}}{-4}$$

Ffactora 10=5\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{5\times 2} fel lluoswm ail israddau \sqrt{5}\sqrt{2}.

$$\frac{-18+6\sqrt{5}+2\sqrt{10}+2\sqrt{5}\sqrt{2}\sqrt{5}}{-4}$$

Lluosi \sqrt{5} a \sqrt{5} i gael 5.

$$\frac{-18+6\sqrt{5}+2\sqrt{10}+2\times 5\sqrt{2}}{-4}$$

Lluosi 2 a 5 i gael 10.

$$\frac{-18+6\sqrt{5}+2\sqrt{10}+10\sqrt{2}}{-4}$$

Ffactor

$$\frac{9 - \sqrt{10} - 3 \sqrt{5} - 5 \sqrt{2}}{2} = -3.9707747022666124$$