003=2xleft(1-100/sqrt{996*10^6}right)-1 eching

$$003 = 2x \left( 1- \frac{ 100 }{ \sqrt{ 996 \times { 10 }^{ 6 } } } \right) -1$$

x uchun yechish

$$x=\frac{10\left(\sqrt{249}+4980\right)}{99599}\approx 0,501589347$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

0 hosil qilish uchun 0 va 0 ni ko'paytirish.

$$0\times 3=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

0 hosil qilish uchun 0 va 3 ni ko'paytirish.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 10^{6}}}\right)-1$$

6 daraja ko‘rsatkichini 10 ga hisoblang va 1000000 ni qiymatni oling.

$$0=2x\left(1-\frac{100}{\sqrt{996\times 1000000}}\right)-1$$

996000000 hosil qilish uchun 996 va 1000000 ni ko'paytirish.

$$0=2x\left(1-\frac{100}{\sqrt{996000000}}\right)-1$$

Faktor: 996000000=2000^{2}\times 249. \sqrt{2000^{2}\times 249} koʻpaytmasining kvadrat ildizini \sqrt{2000^{2}}\sqrt{249} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2000^{2} ning kvadrat ildizini chiqarish.

$$0=2x\left(1-\frac{100}{2000\sqrt{249}}\right)-1$$

\frac{100}{2000\sqrt{249}} maxrajini \sqrt{249} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

\sqrt{249} kvadrati – 249.

$$0=2x\left(1-\frac{100\sqrt{249}}{2000\times 249}\right)-1$$

Surat va maxrajdagi ikkala 100 ni qisqartiring.

$$0=2x\left(1-\frac{\sqrt{249}}{20\times 249}\right)-1$$

4980 hosil qilish uchun 20 va 249 ni ko'paytirish.

$$0=2x\left(1-\frac{\sqrt{249}}{4980}\right)-1$$

2x ga 1-\frac{\sqrt{249}}{4980} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0=2x+2x\left(-\frac{\sqrt{249}}{4980}\right)-1$$

2 va 4980 ichida eng katta umumiy 4980 faktorini bekor qiling.

$$0=2x+\frac{\sqrt{249}}{-2490}x-1$$

\frac{\sqrt{249}}{-2490}x ni yagona kasrga aylantiring.

$$0=2x+\frac{\sqrt{249}x}{-2490}-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x+\frac{\sqrt{249}x}{-2490}-1=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$2x+\frac{\sqrt{249}x}{-2490}=1$$

Tenglamaning ikkala tarafini -2490 ga ko'paytirish.

$$-4980x+\sqrt{249}x=-2490$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-4980+\sqrt{249}\right)x=-2490$$

Tenglama standart shaklda.

$$\left(\sqrt{249}-4980\right)x=-2490$$

Ikki tarafini -4980+\sqrt{249} ga bo‘ling.

$$\frac{\left(\sqrt{249}-4980\right)x}{\sqrt{249}-4980}=-\frac{2490}{\sqrt{249}-4980}$$

-4980+\sqrt{249} ga bo'lish -4980+\sqrt{249} ga ko'paytirishni bekor qiladi.

$$x=-\frac{2490}{\sqrt{249}-4980}$$

-2490 ni -4980+\sqrt{249} ga bo'lish.

$$x=\frac{10\sqrt{249}+49800}{99599}$$