x^4-5x^2-75/4=0 eching

$$x ^ { 4 } - 5 x ^ { 2 } - \frac { 75 } { 4 } = 0$$

x uchun yechish (complex solution)

$$x = \frac{\sqrt{30}}{2} \approx 2,738612788$$

$$x = -\frac{\sqrt{30}}{2} \approx -2,738612788$$

$$x=-\frac{\sqrt{10}i}{2}\approx -0-1,58113883i$$

$$x=\frac{\sqrt{10}i}{2}\approx 1,58113883i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-5t-\frac{75}{4}=0$$

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 -\frac{75}{4} ni ayiring.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-\frac{75}{4}\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{5±10}{2}$$

t=\frac{5±10}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{15}{2} t=-\frac{5}{2}$$

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

$$x=-\frac{\sqrt{30}}{2} x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{10}i}{2} x=\frac{\sqrt{10}i}{2}$$

x uchun yechish

$$x = -\frac{\sqrt{30}}{2} \approx -2,738612788$$

$$x = \frac{\sqrt{30}}{2} \approx 2,738612788$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-5t-\frac{75}{4}=0$$

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 -\frac{75}{4} ni ayiring.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-\frac{75}{4}\right)}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{5±10}{2}$$

t=\frac{5±10}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{15}{2} t=-\frac{5}{2}$$

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

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$