4x^2-2=16 eching

$$4 x ^ { 2 } - 2 = 16$$

x uchun yechish

$$x = \frac{3 \sqrt{2}}{2} \approx 2,121320344$$

$$x = -\frac{3 \sqrt{2}}{2} \approx -2,121320344$$

Kvadrat ildizini topish bo'yicha qadamlar

2 ni ikki tarafga qo’shing.

$$4x^{2}=16+2$$

18 olish uchun 16 va 2'ni qo'shing.

$$4x^{2}=18$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{18}{4}$$

\frac{18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{9}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 16 ni ayirish.

$$4x^{2}-2-16=0$$

-18 olish uchun -2 dan 16 ni ayirish.

$$4x^{2}-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va -18 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-18\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-18\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-18\right)}}{2\times 4}$$

-16 ni -18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{288}}{2\times 4}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{2}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{2}}{8}$$

x=\frac{0±12\sqrt{2}}{8} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±12\sqrt{2}}{8} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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