x^6-19x^3-216=0 eching

$$x ^ { 6 } - 19 x ^ { 3 } - 216 = 0$$

x uchun yechish (complex solution)

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

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-19t-216=0$$

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 -19 ni va c uchun -216 ni ayiring.

$$t=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 1\left(-216\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{19±35}{2}$$

t=\frac{19±35}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=27 t=-8$$

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

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

x uchun yechish

$$x=-2$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{3} uchun t ni almashtiring.

$$t^{2}-19t-216=0$$

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 -19 ni va c uchun -216 ni ayiring.

$$t=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 1\left(-216\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{19±35}{2}$$

t=\frac{19±35}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=27 t=-8$$

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

$$x=3 x=-2$$