x^6-7x^3-8=0 eching

$$x ^ { 6 } - 7 x ^ { 3 } - 8 = 0$$

x uchun yechish (complex solution)

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

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-7t-8=0$$

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 -7 ni va c uchun -8 ni ayiring.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\left(-8\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{7±9}{2}$$

t=\frac{7±9}{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.

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

x uchun yechish

$$x=-1$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-7t-8=0$$

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 -7 ni va c uchun -8 ni ayiring.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\left(-8\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{7±9}{2}$$

t=\frac{7±9}{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.

$$x=2 x=-1$$