Issolvi frac{sqrt{-2}+1}{sqrt{-2}-1}

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

Evalwa

$$\text{Indeterminate}$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{-2}+1}{\sqrt{-2}-1} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{-2}+1.

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

Ikkunsidra li \left(\sqrt{-2}-1\right)\left(\sqrt{-2}+1\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra \sqrt{-2}. Ikkwadra 1.

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

Naqqas 1 minn -2 biex tikseb -3.

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

Immultiplika \sqrt{-2}+1 u \sqrt{-2}+1 biex tikseb \left(\sqrt{-2}+1\right)^{2}.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{-2}+1\right)^{2}.

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

Ikkalkula \sqrt{-2} bil-power ta' 2 u tikseb -2.

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

Żid -2 u 1 biex tikseb -1.

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

Immultiplika kemm in-numeratur u kif ukoll id-denominatur b’-1.

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

Evalwa (complex solution)

$$\frac{-2\sqrt{2}i+1}{3}\approx 0.333333333-0.942809042i$$

Parti Reali (complex solution)

$$\frac{1}{3} = 0.3333333333333333$$