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

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

x uchun yechish (complex solution)

$$x=\frac{i\sqrt{10\left(\sqrt{161}+1\right)}}{20}\approx 0,584990973i$$

$$x=-\frac{i\sqrt{10\left(\sqrt{161}+1\right)}}{20}\approx -0-0,584990973i$$

$$x=-\frac{\sqrt{10\left(\sqrt{161}-1\right)}}{20}\approx -0,540568625$$

$$x=\frac{\sqrt{10\left(\sqrt{161}-1\right)}}{20}\approx 0,540568625$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 20 ni, b uchun 1 ni va c uchun -2 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{-1±\sqrt{161}}{40}$$

t=\frac{-1±\sqrt{161}}{40} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{161}-1}{40} t=\frac{-\sqrt{161}-1}{40}$$

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

$$x=-\sqrt{\frac{\sqrt{161}-1}{40}} x=\sqrt{\frac{\sqrt{161}-1}{40}} x=-i\sqrt{\frac{\sqrt{161}+1}{40}} x=i\sqrt{\frac{\sqrt{161}+1}{40}}$$

x uchun yechish

$$x=-\frac{\sqrt{10\left(\sqrt{161}-1\right)}}{20}\approx -0,540568625$$

$$x=\frac{\sqrt{10\left(\sqrt{161}-1\right)}}{20}\approx 0,540568625$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 20 ni, b uchun 1 ni va c uchun -2 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{-1±\sqrt{161}}{40}$$

t=\frac{-1±\sqrt{161}}{40} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{161}-1}{40} t=\frac{-\sqrt{161}-1}{40}$$

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

$$x=\frac{\sqrt{\frac{\sqrt{161}-1}{10}}}{2} x=-\frac{\sqrt{\frac{\sqrt{161}-1}{10}}}{2}$$