Issolvi 7/-10-sqrt{2}

$$\frac { 7 } { - 10 - \sqrt { 2 } }$$

Evalwa

$$\frac{\sqrt{2}-10}{14}\approx -0.61327046$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{7}{-10-\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill--10+\sqrt{2}.

$$\frac{7\left(-10+\sqrt{2}\right)}{\left(-10-\sqrt{2}\right)\left(-10+\sqrt{2}\right)}$$

Ikkunsidra li \left(-10-\sqrt{2}\right)\left(-10+\sqrt{2}\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}.

$$\frac{7\left(-10+\sqrt{2}\right)}{\left(-10\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

Ikkwadra -10. Ikkwadra \sqrt{2}.

$$\frac{7\left(-10+\sqrt{2}\right)}{100-2}$$

Naqqas 2 minn 100 biex tikseb 98.

$$\frac{7\left(-10+\sqrt{2}\right)}{98}$$

Iddividi 7\left(-10+\sqrt{2}\right) b'98 biex tikseb\frac{1}{14}\left(-10+\sqrt{2}\right).

$$\frac{1}{14}\left(-10+\sqrt{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{14} b'-10+\sqrt{2}.

$$\frac{1}{14}\left(-10\right)+\frac{1}{14}\sqrt{2}$$

Immultiplika \frac{1}{14} u -10 biex tikseb \frac{-10}{14}.

$$\frac{-10}{14}+\frac{1}{14}\sqrt{2}$$

Naqqas il-frazzjoni \frac{-10}{14} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$-\frac{5}{7}+\frac{1}{14}\sqrt{2}$$