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

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

x uchun yechish (complex solution)

$$x=-\sqrt{2}i\approx -0-1,414213562i$$

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

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$x^{2}+2=0$$

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Tenglama yechildi.

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

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga ko'paytirish.

$$x^{2}+2=0$$

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

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

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8}}{2}$$

-8 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{2}i}{2}$$

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

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

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

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

Tenglama yechildi.

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