(2x-1)^2=8 eching

$$( 2 x - 1 ) ^ { 2 } = 8$$

x uchun yechish

$$x=\sqrt{2}+\frac{1}{2}\approx 1,914213562$$

$$x=\frac{1}{2}-\sqrt{2}\approx -0,914213562$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

1 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -1 ayirilsa 0 qoladi.

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

2\sqrt{2} dan -1 ni ayirish.

$$2x=2\sqrt{2}+1$$

-2\sqrt{2} dan -1 ni ayirish.

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

Ikki tarafini 2 ga bo‘ling.

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

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

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

2\sqrt{2}+1 ni 2 ga bo'lish.

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

-2\sqrt{2}+1 ni 2 ga bo'lish.

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

Tenglama yechildi.

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