sqrt{2}x-1/sqrt{2}=sqrt{8}x eching

$$\sqrt { 2 } x - \frac { 1 } { \sqrt { 2 } } = \sqrt { 8 } x$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\sqrt{2}x-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\sqrt{8}x$$

\sqrt{2} kvadrati – 2.

$$\sqrt{2}x-\frac{\sqrt{2}}{2}=\sqrt{8}x$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\sqrt{2}x-\frac{\sqrt{2}}{2}=2\sqrt{2}x$$

Ikkala tarafdan 2\sqrt{2}x ni ayirish.

$$\sqrt{2}x-\frac{\sqrt{2}}{2}-2\sqrt{2}x=0$$

-\sqrt{2}x ni olish uchun \sqrt{2}x va -2\sqrt{2}x ni birlashtirish.

$$-\sqrt{2}x-\frac{\sqrt{2}}{2}=0$$

\frac{\sqrt{2}}{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-\sqrt{2}x=\frac{\sqrt{2}}{2}$$

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$-2\sqrt{2}x=\sqrt{2}$$

Tenglama standart shaklda.

$$\left(-2\sqrt{2}\right)x=\sqrt{2}$$

Ikki tarafini -2\sqrt{2} ga bo‘ling.

$$\frac{\left(-2\sqrt{2}\right)x}{-2\sqrt{2}}=\frac{\sqrt{2}}{-2\sqrt{2}}$$

-2\sqrt{2} ga bo'lish -2\sqrt{2} ga ko'paytirishni bekor qiladi.

$$x=\frac{\sqrt{2}}{-2\sqrt{2}}$$

\sqrt{2} ni -2\sqrt{2} ga bo'lish.

$$x=-\frac{1}{2}$$