Datrys frac{3-sqrt{2}}{(1-sqrt{5}}

$$\frac{ 3- \sqrt{ 2 } }{ (1- \sqrt{ 5 } }$$

Enrhifo

$$\frac{\sqrt{2}+\sqrt{10}-3\sqrt{5}-3}{4}\approx -1.282928177$$

Camau Ateb

Mae'n rhesymoli enwadur \frac{3-\sqrt{2}}{1-\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â 1+\sqrt{5}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}$$

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}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{1^{2}-\left(\sqrt{5}\right)^{2}}$$

Sgwâr 1. Sgwâr \sqrt{5}.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{1-5}$$

Tynnu 5 o 1 i gael -4.

$$\frac{\left(3-\sqrt{2}\right)\left(1+\sqrt{5}\right)}{-4}$$

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 3-\sqrt{2} gan bob 1+\sqrt{5}.

$$\frac{3+3\sqrt{5}-\sqrt{2}-\sqrt{2}\sqrt{5}}{-4}$$

I luosi \sqrt{2} a \sqrt{5}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{3+3\sqrt{5}-\sqrt{2}-\sqrt{10}}{-4}$$

Lluosi'r rhifiadur a’r enwadur â -1.

$$\frac{-3-3\sqrt{5}+\sqrt{2}+\sqrt{10}}{4}$$