-40-5b^2+b^4=0 eching

$$- 40 - 5 b ^ { 2 } + b ^ { 4 } = 0$$

b uchun yechish

$$b = -\frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx -3,049710684$$

$$b = \frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx 3,049710684$$

Kvadrat tenglamalaridan foydalanish qoidalari

b^{2} uchun t ni almashtiring.

$$t^{2}-5t-40=0$$

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 -5 ni va c uchun -40 ni ayiring.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-40\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{5±\sqrt{185}}{2}$$

t=\frac{5±\sqrt{185}}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{185}+5}{2} t=\frac{5-\sqrt{185}}{2}$$

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

$$b=\frac{\sqrt{2\sqrt{185}+10}}{2} b=-\frac{\sqrt{2\sqrt{185}+10}}{2}$$