4+sqrt{2}x^2=2 eching

$$4+ \sqrt{ 2 } { x }^{ 2 } =2$$

x uchun yechish (complex solution)

$$x=-\sqrt[4]{2}i\approx -0-1,189207115i$$

$$x=\sqrt[4]{2}i\approx 1,189207115i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 4 ni ayirish.

$$\sqrt{2}x^{2}=2-4$$

-2 olish uchun 2 dan 4 ni ayirish.

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

\sqrt{2} ga bo'lish \sqrt{2} ga ko'paytirishni bekor qiladi.

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

-2 ni \sqrt{2} ga bo'lish.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt[4]{2}i x=-\sqrt[4]{2}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2 ni ayirish.

$$4+\sqrt{2}x^{2}-2=0$$

2 olish uchun 4 dan 2 ni ayirish.

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

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.

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

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

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

0 kvadratini chiqarish.

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

-4 ni \sqrt{2} marotabaga ko'paytirish.

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

-4\sqrt{2} ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\sqrt{2}}}{2\sqrt{2}}$$

-8\sqrt{2} ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\times 2^{\frac{3}{4}}i}{2\sqrt{2}}$$

x=\frac{0±2\times 2^{\frac{3}{4}}i}{2\sqrt{2}} tenglamasini yeching, bunda ± musbat.

$$x=\frac{2i}{2^{\frac{3}{4}}}$$

x=\frac{0±2\times 2^{\frac{3}{4}}i}{2\sqrt{2}} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt[4]{2}i$$

Tenglama yechildi.

$$x=\frac{2i}{2^{\frac{3}{4}}} x=-\sqrt[4]{2}i$$