x^6-9x^3+8=0 eching

$${ x }^{ 6 } -9 { x }^{ 3 } +8=0$$

x uchun yechish (complex solution)

$$x\in 2,-1+\sqrt{3}i,-\sqrt{3}i-1,\frac{-1+\sqrt{3}i}{2},1,\frac{-\sqrt{3}i-1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-9t+8=0$$

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 -9 ni va c uchun 8 ni ayiring.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 1\times 8}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{9±7}{2}$$

t=\frac{9±7}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=8 t=1$$

x=t^{3} boʻlganda, yechimlar har bir t uchun tenglamani yechish orqali olinadi.

$$x=-1+\sqrt{3}i x=-\sqrt{3}i-1 x=2 x=\frac{-1+\sqrt{3}i}{2} x=\frac{-\sqrt{3}i-1}{2} x=1$$

x uchun yechish

$$x=1$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-9t+8=0$$

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 -9 ni va c uchun 8 ni ayiring.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 1\times 8}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{9±7}{2}$$

t=\frac{9±7}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=8 t=1$$

x=t^{3} boʻlganda, yechimlar har bir t uchun x=\sqrt[3]{t} hisoblanishi orqali olinadi.

$$x=2 x=1$$