1/4x^2+1/4=0 eching

$$\frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 4 } = 0$$

x uchun yechish (complex solution)

$$x=-i$$

$$x=i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{4} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikki tarafini 4 va teskari kasri \frac{1}{4} ga ko‘paytiring.

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

-1 hosil qilish uchun -\frac{1}{4} va 4 ni ko'paytirish.

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

Tenglama yechildi.

$$x=i x=-i$$

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.

$$\frac{1}{4}x^{2}+\frac{1}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{4} ni a, 0 ni b va \frac{1}{4} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\times \frac{1}{4}}}{2\times \frac{1}{4}}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\times \frac{1}{4}}}{2\times \frac{1}{4}}$$

-4 ni \frac{1}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{1}{4}}}{2\times \frac{1}{4}}$$

-\frac{1}{4} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{1}{2}i}{2\times \frac{1}{4}}$$

2 ni \frac{1}{4} marotabaga ko'paytirish.

$$x=\frac{0±\frac{1}{2}i}{\frac{1}{2}}$$

x=\frac{0±\frac{1}{2}i}{\frac{1}{2}} tenglamasini yeching, bunda ± musbat.

$$x=i$$

x=\frac{0±\frac{1}{2}i}{\frac{1}{2}} tenglamasini yeching, bunda ± manfiy.

$$x=-i$$

Tenglama yechildi.

$$x=i x=-i$$