4x^2-16=0 eching

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

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 4 ga bo‘ling.

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

Hisoblang: x^{2}-4. x^{2}-4 ni x^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Tenglamani yechish uchun x-2=0 va x+2=0 ni yeching.

$$x=2 x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

16 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{16}{4}$$

4 ni olish uchun 16 ni 4 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

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 -16 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

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

-16 ni -16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{256}}{2\times 4}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{0±16}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±16}{8}$$

x=\frac{0±16}{8} tenglamasini yeching, bunda ± musbat. 16 ni 8 ga bo'lish.

$$x=2$$

x=\frac{0±16}{8} tenglamasini yeching, bunda ± manfiy. -16 ni 8 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$