2x^4-10x^2-8=0 eching

$$2 x ^ { 4 } - 10 x ^ { 2 } - 8 = 0$$

x uchun yechish (complex solution)

$$x=\frac{i\sqrt{2\left(\sqrt{41}-5\right)}}{2}\approx 0,837593051i$$

$$x=-\frac{i\sqrt{2\left(\sqrt{41}-5\right)}}{2}\approx -0-0,837593051i$$

$$x = -\frac{\sqrt{2 {(\sqrt{41} + 5)}}}{2} \approx -2,387794405$$

$$x = \frac{\sqrt{2 {(\sqrt{41} + 5)}}}{2} \approx 2,387794405$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$2t^{2}-10t-8=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 2 ni, b uchun -10 ni va c uchun -8 ni ayiring.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Hisoblarni amalga oshiring.

$$t=\frac{10±2\sqrt{41}}{4}$$

t=\frac{10±2\sqrt{41}}{4} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{41}+5}{2} t=\frac{5-\sqrt{41}}{2}$$

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

$$x=-\sqrt{\frac{\sqrt{41}+5}{2}} x=\sqrt{\frac{\sqrt{41}+5}{2}} x=-i\sqrt{-\frac{5-\sqrt{41}}{2}} x=i\sqrt{-\frac{5-\sqrt{41}}{2}}$$

x uchun yechish

$$x = -\frac{\sqrt{2 {(\sqrt{41} + 5)}}}{2} \approx -2,387794405$$

$$x = \frac{\sqrt{2 {(\sqrt{41} + 5)}}}{2} \approx 2,387794405$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$2t^{2}-10t-8=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 2 ni, b uchun -10 ni va c uchun -8 ni ayiring.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Hisoblarni amalga oshiring.

$$t=\frac{10±2\sqrt{41}}{4}$$

t=\frac{10±2\sqrt{41}}{4} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{41}+5}{2} t=\frac{5-\sqrt{41}}{2}$$

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

$$x=\frac{\sqrt{2\sqrt{41}+10}}{2} x=-\frac{\sqrt{2\sqrt{41}+10}}{2}$$