x^4-6x^2-27=0 eching

$$x ^ { 4 } - 6 x ^ { 2 } - 27 = 0$$

x uchun yechish (complex solution)

$$x=3$$

$$x=-3$$

$$x=-\sqrt{3}i\approx -0-1,732050808i$$

$$x=\sqrt{3}i\approx 1,732050808i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-6t-27=0$$

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 -6 ni va c uchun -27 ni ayiring.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-27\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{6±12}{2}$$

t=\frac{6±12}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=9 t=-3$$

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

$$x=-3 x=3 x=-\sqrt{3}i x=\sqrt{3}i$$

x uchun yechish

$$x=-3$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-6t-27=0$$

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 -6 ni va c uchun -27 ni ayiring.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-27\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{6±12}{2}$$

t=\frac{6±12}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=9 t=-3$$

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

$$x=3 x=-3$$