x^4-20x^2-19=0 eching

$${ x }^{ 4 } -20 { x }^{ 2 } -19=0$$

x uchun yechish (complex solution)

$$x=i\sqrt{\sqrt{119}-10}\approx 0,953263927i$$

$$x=-i\sqrt{\sqrt{119}-10}\approx -0-0,953263927i$$

$$x=-\sqrt{\sqrt{119}+10}\approx -4,572604522$$

$$x=\sqrt{\sqrt{119}+10}\approx 4,572604522$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-20t-19=0$$

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 -20 ni va c uchun -19 ni ayiring.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-19\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{20±2\sqrt{119}}{2}$$

t=\frac{20±2\sqrt{119}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\sqrt{119}+10 t=10-\sqrt{119}$$

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

$$x=-\sqrt{\sqrt{119}+10} x=\sqrt{\sqrt{119}+10} x=-i\sqrt{-\left(10-\sqrt{119}\right)} x=i\sqrt{-\left(10-\sqrt{119}\right)}$$

x uchun yechish

$$x=-\sqrt{\sqrt{119}+10}\approx -4,572604522$$

$$x=\sqrt{\sqrt{119}+10}\approx 4,572604522$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-20t-19=0$$

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 -20 ni va c uchun -19 ni ayiring.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-19\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{20±2\sqrt{119}}{2}$$

t=\frac{20±2\sqrt{119}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\sqrt{119}+10 t=10-\sqrt{119}$$

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

$$x=\sqrt{\sqrt{119}+10} x=-\sqrt{\sqrt{119}+10}$$