x^8-3x^4+2=0 eching

$${ x }^{ 8 } -3 { x }^{ 4 } +2=0$$

x uchun yechish (complex solution)

$$x\in \sqrt[4]{2},-\sqrt[4]{2}i,\sqrt[4]{2}i,-\sqrt[4]{2},-1,1,i,-i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{4} uchun t ni almashtiring.

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

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 -3 ni va c uchun 2 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{3±1}{2}$$

t=\frac{3±1}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=2 t=1$$

x=t^{4} boʻlganda, yechimlar har bir t uchun tenglamani yechish orqali olinadi.

$$x=-\sqrt[4]{2}i x=-\sqrt[4]{2} x=\sqrt[4]{2}i x=\sqrt[4]{2} x=-1 x=-i x=i x=1$$

x uchun yechish

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

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

$$x=1$$

$$x=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{4} uchun t ni almashtiring.

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

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 -3 ni va c uchun 2 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{3±1}{2}$$

t=\frac{3±1}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=2 t=1$$

x=t^{4} boʻlganda, yechimlar musbat t uchun x=±\sqrt[4]{t} hisoblanishi orqali olinadi.

$$x=\sqrt[4]{2} x=-\sqrt[4]{2} x=1 x=-1$$