x^4-8x^2-4=0 eching

$${ x }^{ 4 } -8 { x }^{ 2 } -4=0$$

x uchun yechish (complex solution)

$$x=i\sqrt{2\left(\sqrt{5}-2\right)}\approx 0,687121499i$$

$$x=-i\sqrt{2\left(\sqrt{5}-2\right)}\approx -0-0,687121499i$$

$$x=-\sqrt{2\left(\sqrt{5}+2\right)}\approx -2,91069338$$

$$x=\sqrt{2\left(\sqrt{5}+2\right)}\approx 2,91069338$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-8t-4=0$$

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 -8 ni va c uchun -4 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{8±4\sqrt{5}}{2}$$

t=\frac{8±4\sqrt{5}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=2\sqrt{5}+4 t=4-2\sqrt{5}$$

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

$$x=-\sqrt{2\sqrt{5}+4} x=\sqrt{2\sqrt{5}+4} x=-i\sqrt{-\left(4-2\sqrt{5}\right)} x=i\sqrt{-\left(4-2\sqrt{5}\right)}$$

x uchun yechish

$$x=-\sqrt{2\left(\sqrt{5}+2\right)}\approx -2,91069338$$

$$x=\sqrt{2\left(\sqrt{5}+2\right)}\approx 2,91069338$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-8t-4=0$$

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 -8 ni va c uchun -4 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{8±4\sqrt{5}}{2}$$

t=\frac{8±4\sqrt{5}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=2\sqrt{5}+4 t=4-2\sqrt{5}$$

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

$$x=\frac{\sqrt{8\sqrt{5}+16}}{2} x=-\frac{\sqrt{8\sqrt{5}+16}}{2}$$