Rešite 2*2/-1+sqrt{5}

$$2 \times \frac{ 2 }{ -1+ \sqrt{ 5 } }$$

Ovrednoti

$$\sqrt{5}+1\approx 3,236067977$$

Koraki rešitve

Racionalizirajte imenovalec \frac{2}{-1+\sqrt{5}} tako, da pomnožite števec in imenovalec s -1-\sqrt{5}.

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

Razmislite o \left(-1+\sqrt{5}\right)\left(-1-\sqrt{5}\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Kvadrat števila -1. Kvadrat števila \sqrt{5}.

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

Odštejte 5 od 1, da dobite -4.

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

Delite 2\left(-1-\sqrt{5}\right) s/z -4, da dobite -\frac{1}{2}\left(-1-\sqrt{5}\right).

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

Uporabite distributivnost, da pomnožite -\frac{1}{2} s/z -1-\sqrt{5}.

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

Pomnožite -\frac{1}{2} in -1, da dobite \frac{1}{2}.

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

Pomnožite -\frac{1}{2} in -1, da dobite \frac{1}{2}.

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

Uporabite distributivnost, da pomnožite 2 s/z \frac{1}{2}+\frac{1}{2}\sqrt{5}.

$$2\times \frac{1}{2}+2\times \frac{1}{2}\sqrt{5}$$

Okrajšaj 2 in 2.

$$1+2\times \frac{1}{2}\sqrt{5}$$

Okrajšaj 2 in 2.

$$1+\sqrt{5}$$

Faktoriziraj

$$\sqrt{5} + 1 = 3,236067977$$