2/5+665sqrt{45} eching

$$\frac{ 2 }{ 5+665 \sqrt{ 45 } }$$

Baholash

$$\frac{399\sqrt{5}-1}{1990010}\approx 0,000447832$$

Yechim qadamlari

Faktor: 45=3^{2}\times 5. \sqrt{3^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{2}{5+665\times 3\sqrt{5}}$$

1995 hosil qilish uchun 665 va 3 ni ko'paytirish.

$$\frac{2}{5+1995\sqrt{5}}$$

\frac{2}{5+1995\sqrt{5}} maxrajini 5-1995\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\left(5-1995\sqrt{5}\right)}{\left(5+1995\sqrt{5}\right)\left(5-1995\sqrt{5}\right)}$$

Hisoblang: \left(5+1995\sqrt{5}\right)\left(5-1995\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(5-1995\sqrt{5}\right)}{5^{2}-\left(1995\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{2\left(5-1995\sqrt{5}\right)}{25-\left(1995\sqrt{5}\right)^{2}}$$

\left(1995\sqrt{5}\right)^{2} ni kengaytirish.

$$\frac{2\left(5-1995\sqrt{5}\right)}{25-1995^{2}\left(\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini 1995 ga hisoblang va 3980025 ni qiymatni oling.

$$\frac{2\left(5-1995\sqrt{5}\right)}{25-3980025\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{2\left(5-1995\sqrt{5}\right)}{25-3980025\times 5}$$

19900125 hosil qilish uchun 3980025 va 5 ni ko'paytirish.

$$\frac{2\left(5-1995\sqrt{5}\right)}{25-19900125}$$

-19900100 olish uchun 25 dan 19900125 ni ayirish.

$$\frac{2\left(5-1995\sqrt{5}\right)}{-19900100}$$

-\frac{1}{9950050}\left(5-1995\sqrt{5}\right) ni olish uchun 2\left(5-1995\sqrt{5}\right) ni -19900100 ga bo‘ling.

$$-\frac{1}{9950050}\left(5-1995\sqrt{5}\right)$$

-\frac{1}{9950050} ga 5-1995\sqrt{5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{1}{9950050}\times 5-\frac{1}{9950050}\left(-1995\right)\sqrt{5}$$

-\frac{1}{9950050}\times 5 ni yagona kasrga aylantiring.

$$\frac{-5}{9950050}-\frac{1}{9950050}\left(-1995\right)\sqrt{5}$$

\frac{-5}{9950050} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1}{1990010}-\frac{1}{9950050}\left(-1995\right)\sqrt{5}$$

-\frac{1}{9950050}\left(-1995\right) ni yagona kasrga aylantiring.

$$-\frac{1}{1990010}+\frac{-\left(-1995\right)}{9950050}\sqrt{5}$$

1995 hosil qilish uchun -1 va -1995 ni ko'paytirish.

$$-\frac{1}{1990010}+\frac{1995}{9950050}\sqrt{5}$$

\frac{1995}{9950050} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1}{1990010}+\frac{399}{1990010}\sqrt{5}$$