x^4-x^2-20=0 eching

$${ x }^{ 4 } - { x }^{ 2 } -20 = 0$$

x uchun yechish (complex solution)

$$x=\sqrt{5}\approx 2,236067977$$

$$x=-\sqrt{5}\approx -2,236067977$$

$$x=-2i$$

$$x=2i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-t-20=0$$

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 -1 ni va c uchun -20 ni ayiring.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{1±9}{2}$$

t=\frac{1±9}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=5 t=-4$$

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

$$x=-\sqrt{5} x=\sqrt{5} x=-2i x=2i$$

x uchun yechish

$$x=-\sqrt{5}\approx -2,236067977$$

$$x=\sqrt{5}\approx 2,236067977$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-t-20=0$$

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 -1 ni va c uchun -20 ni ayiring.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{1±9}{2}$$

t=\frac{1±9}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=5 t=-4$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$