-4x^2+1=0 eching

$$-4 { x }^{ 2 } +1=0$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=-\frac{1}{2}=-0,5$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-4x^{2}=-1$$

Ikki tarafini -4 ga bo‘ling.

$$x^{2}=\frac{-1}{-4}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-4} kasrini \frac{1}{4} ga soddalashtirish mumkin.

$$x^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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.

$$-4x^{2}+1=0$$

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 1 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

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

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±4}{-8}$$

x=\frac{0±4}{-8} tenglamasini yeching, bunda ± musbat. \frac{4}{-8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{0±4}{-8} tenglamasini yeching, bunda ± manfiy. \frac{-4}{-8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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