frac{100sqrt{3}}{1-sqrt{3}}=x eching

$$\frac{ 100 \sqrt{ 3 } }{ 1- \sqrt{ 3 } } =x$$

x uchun yechish

$$x=-50\sqrt{3}-150\approx -236,602540378$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{100\sqrt{3}}{1-\sqrt{3}} maxrajini 1+\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)}=x$$

Hisoblang: \left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{1^{2}-\left(\sqrt{3}\right)^{2}}=x$$

1 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{1-3}=x$$

-2 olish uchun 1 dan 3 ni ayirish.

$$\frac{100\sqrt{3}\left(1+\sqrt{3}\right)}{-2}=x$$

100\sqrt{3} ga 1+\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{100\sqrt{3}+100\left(\sqrt{3}\right)^{2}}{-2}=x$$

\sqrt{3} kvadrati – 3.

$$\frac{100\sqrt{3}+100\times 3}{-2}=x$$

300 hosil qilish uchun 100 va 3 ni ko'paytirish.

$$\frac{100\sqrt{3}+300}{-2}=x$$

-50\sqrt{3}-150 natijani olish uchun 100\sqrt{3}+300 ning har bir ifodasini -2 ga bo‘ling.

$$-50\sqrt{3}-150=x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x=-50\sqrt{3}-150$$