y=4x(1-2500/sqrt{996*10^6})-1 eching

$$y=4x(1- \frac{ 2500 }{ \sqrt{ 996 \times { 10 }^{ 6 } } } )-1$$

x uchun yechish

$$x=\frac{\left(5\sqrt{249}+996\right)\left(y+1\right)}{3959}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$y=4x\left(1-\frac{2500}{\sqrt{996\times 1000000}}\right)-1$$

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

$$y=4x\left(1-\frac{2500}{\sqrt{996000000}}\right)-1$$

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.

$$y=4x\left(1-\frac{2500}{2000\sqrt{249}}\right)-1$$

\frac{2500}{2000\sqrt{249}} maxrajini \sqrt{249} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$y=4x\left(1-\frac{2500\sqrt{249}}{2000\left(\sqrt{249}\right)^{2}}\right)-1$$

\sqrt{249} kvadrati – 249.

$$y=4x\left(1-\frac{2500\sqrt{249}}{2000\times 249}\right)-1$$

Surat va maxrajdagi ikkala 500 ni qisqartiring.

$$y=4x\left(1-\frac{5\sqrt{249}}{4\times 249}\right)-1$$

996 hosil qilish uchun 4 va 249 ni ko'paytirish.

$$y=4x\left(1-\frac{5\sqrt{249}}{996}\right)-1$$

4x ga 1-\frac{5\sqrt{249}}{996} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=4x+4x\left(-\frac{5\sqrt{249}}{996}\right)-1$$

4 va 996 ichida eng katta umumiy 996 faktorini bekor qiling.

$$y=4x+\frac{5\sqrt{249}}{-249}x-1$$

\frac{5\sqrt{249}}{-249}x ni yagona kasrga aylantiring.

$$y=4x+\frac{5\sqrt{249}x}{-249}-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$4x+\frac{5\sqrt{249}x}{-249}-1=y$$

1 ni ikki tarafga qo’shing.

$$4x+\frac{5\sqrt{249}x}{-249}=y+1$$

Tenglamaning ikkala tarafini -249 ga ko'paytirish.

$$-996x+5\sqrt{249}x=-249y-249$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-996+5\sqrt{249}\right)x=-249y-249$$

Tenglama standart shaklda.

$$\left(5\sqrt{249}-996\right)x=-249y-249$$

Ikki tarafini -996+5\sqrt{249} ga bo‘ling.

$$\frac{\left(5\sqrt{249}-996\right)x}{5\sqrt{249}-996}=\frac{-249y-249}{5\sqrt{249}-996}$$

-996+5\sqrt{249} ga bo'lish -996+5\sqrt{249} ga ko'paytirishni bekor qiladi.

$$x=\frac{-249y-249}{5\sqrt{249}-996}$$

-249y-249 ni -996+5\sqrt{249} ga bo'lish.

$$x=\frac{\left(5\sqrt{249}+996\right)\left(y+1\right)}{3959}$$

y uchun yechish

$$y=-\frac{5\sqrt{249}x}{249}+4x-1$$