22x+1/x+1-sqrt{2}=0 eching

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

x uchun yechish

$$x=\frac{\sqrt{2}-3}{7}\approx -0,22654092$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x+1 ga ko'paytirish.

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

2 ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x+2-\sqrt{2}\left(x+1\right)=0$$

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

$$4x+2-\sqrt{2}x-\sqrt{2}=0$$

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$4x-\sqrt{2}x-\sqrt{2}=-2$$

\sqrt{2} ni ikki tarafga qo’shing.

$$4x-\sqrt{2}x=-2+\sqrt{2}$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4-\sqrt{2}\right)x=-2+\sqrt{2}$$

Tenglama standart shaklda.

$$\left(4-\sqrt{2}\right)x=\sqrt{2}-2$$

Ikki tarafini 4-\sqrt{2} ga bo‘ling.

$$\frac{\left(4-\sqrt{2}\right)x}{4-\sqrt{2}}=\frac{\sqrt{2}-2}{4-\sqrt{2}}$$

4-\sqrt{2} ga bo'lish 4-\sqrt{2} ga ko'paytirishni bekor qiladi.

$$x=\frac{\sqrt{2}-2}{4-\sqrt{2}}$$

-2+\sqrt{2} ni 4-\sqrt{2} ga bo'lish.

$$x=\frac{\sqrt{2}-3}{7}$$