Datrys 3-4/3+sqrt{5}

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

Enrhifo

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

Camau Ateb

Mae'n rhesymoli enwadur \frac{4}{3+\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â 3-\sqrt{5}.

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

Ystyriwch \left(3+\sqrt{5}\right)\left(3-\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}.

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

Sgwâr 3. Sgwâr \sqrt{5}.

$$3-\frac{4\left(3-\sqrt{5}\right)}{9-5}$$

Tynnu 5 o 9 i gael 4.

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

Canslo 4 a 4.

$$3-\left(3-\sqrt{5}\right)$$

I ddod o hyd i wrthwyneb 3-\sqrt{5}, dewch o hyd i wrthwyneb pob term.

$$3-3-\left(-\sqrt{5}\right)$$

Gwrthwyneb -\sqrt{5} yw \sqrt{5}.

$$3-3+\sqrt{5}$$

Tynnu 3 o 3 i gael 0.

$$\sqrt{5}$$