x^4-2x^2-1=0 eching

$$x ^ { 4 } - 2 x ^ { 2 } - 1 = 0$$

x uchun yechish (complex solution)

$$x=i\sqrt{\sqrt{2}-1}\approx 0,643594253i$$

$$x=-i\sqrt{\sqrt{2}-1}\approx -0-0,643594253i$$

$$x=-\sqrt{\sqrt{2}+1}\approx -1,553773974$$

$$x=\sqrt{\sqrt{2}+1}\approx 1,553773974$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-2t-1=0$$

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 -2 ni va c uchun -1 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{2±2\sqrt{2}}{2}$$

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

$$t=\sqrt{2}+1 t=1-\sqrt{2}$$

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

$$x=-\sqrt{\sqrt{2}+1} x=\sqrt{\sqrt{2}+1} x=-i\sqrt{-\left(1-\sqrt{2}\right)} x=i\sqrt{-\left(1-\sqrt{2}\right)}$$

x uchun yechish

$$x=-\sqrt{\sqrt{2}+1}\approx -1,553773974$$

$$x=\sqrt{\sqrt{2}+1}\approx 1,553773974$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-2t-1=0$$

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 -2 ni va c uchun -1 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{2±2\sqrt{2}}{2}$$

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

$$t=\sqrt{2}+1 t=1-\sqrt{2}$$

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

$$x=\sqrt{\sqrt{2}+1} x=-\sqrt{\sqrt{2}+1}$$