4x^2-8=0 eching

$$4 x ^ { 2 } - 8 = 0$$

x uchun yechish

$$x=\sqrt{2}\approx 1,414213562$$

$$x=-\sqrt{2}\approx -1,414213562$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$4x^{2}=8$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{8}{4}$$

2 ni olish uchun 8 ni 4 ga bo‘ling.

$$x^{2}=2$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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.

$$4x^{2}-8=0$$

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 -8 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-8\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-8\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-8\right)}}{2\times 4}$$

-16 ni -8 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{128}}{2\times 4}$$

128 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{2}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{2}}{8}$$

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

$$x=\sqrt{2}$$

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

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

Tenglama yechildi.

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