x^2+3x=-x^4 eching

$$x ^ { 2 } + 3 x = - x ^ { 4 }$$

x uchun yechish (complex solution)

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{741}-27}-\sqrt[3]{\sqrt{741}+27}\right)}{18}\approx -1,213411663$$

$$x=0$$

$$x=\frac{18^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(2\sqrt[3]{\sqrt{741}+27}+\sqrt[3]{\sqrt{741}-27}+\sqrt[3]{9\left(\sqrt{247}-9\sqrt{3}\right)}i\right)}{72}\approx 0,606705831+1,450612249i$$

$$x=\frac{18^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{9\left(\sqrt{247}-9\sqrt{3}\right)}i+2\sqrt[3]{\sqrt{741}+27}+\sqrt[3]{\sqrt{741}-27}\right)}{72}\approx 0,606705831-1,450612249i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{4} ni ikki tarafga qo’shing.

$$x^{2}+3x+x^{4}=0$$

x^{2} uchun t ni almashtiring.

$$t^{2}+t+3=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 1 ni, b uchun 1 ni va c uchun 3 ni ayiring.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\times 3}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{-1±\sqrt{-11}}{2}$$

t=\frac{-1±\sqrt{-11}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{-1+\sqrt{11}i}{2} t=\frac{-\sqrt{11}i-1}{2}$$

x=t^{2} boʻlganda, yechimlar har bir t uchun x=±\sqrt{t} hisoblanishi orqali olinadi.

$$x=\sqrt[4]{3}e^{\frac{-\arctan(\sqrt{11})i+3\pi i}{2}} x=\sqrt[4]{3}e^{\frac{-\arctan(\sqrt{11})i+\pi i}{2}} x=\sqrt[4]{3}e^{\frac{\arctan(\sqrt{11})i+3\pi i}{2}} x=\sqrt[4]{3}e^{\frac{\left(\arctan(\sqrt{11})+\pi \right)i}{2}}$$

x uchun yechish

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{741}-27}-\sqrt[3]{\sqrt{741}+27}\right)}{18}\approx -1,213411663$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{4} ni ikki tarafga qo’shing.

$$x^{2}+3x+x^{4}=0$$

x^{2} uchun t ni almashtiring.

$$t^{2}+t+3=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 1 ni, b uchun 1 ni va c uchun 3 ni ayiring.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\times 3}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{-1±\sqrt{-11}}{2}$$

Manfiy sonning kvadrat ildizi real maydonda aniqlanmaydi, bu yerda yechim yo‘q.

$$t\in \emptyset$$

t=x^{2} boʻlganda, asl tenglamada hech qanday yechim yoʻq.

$$x\in \emptyset$$