Datrys frac{-3+2sqrt{2}}{1-sqrt{2}}=

$$\frac { - 3 + 2 \sqrt { 2 } } { 1 - \sqrt { 2 } } =$$

Enrhifo

$$\sqrt{2}-1\approx 0.414213562$$

Camau Ateb

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

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

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

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

Sgwâr 1. Sgwâr \sqrt{2}.

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

Tynnu 2 o 1 i gael -1.

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

Mae unrhyw beth sy'n cael ei rannu â -1 yn rhoi'r gwrthwyneb.

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

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

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

Cyfuno -3\sqrt{2} a 2\sqrt{2} i gael -\sqrt{2}.

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

Sgwâr \sqrt{2} yw 2.

$$-\left(-3-\sqrt{2}+2\times 2\right)$$

Lluosi 2 a 2 i gael 4.

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

Adio -3 a 4 i gael 1.

$$-\left(1-\sqrt{2}\right)$$

I ddod o hyd i wrthwyneb 1-\sqrt{2}, dewch o hyd i wrthwyneb pob term.

$$-1-\left(-\sqrt{2}\right)$$

Gwrthwyneb -\sqrt{2} yw \sqrt{2}.

$$-1+\sqrt{2}$$