4x^4+19x^2-5=0 eching

$$4 x ^ { 4 } + 19 x ^ { 2 } - 5 = 0$$

x uchun yechish (complex solution)

$$x=\frac{1}{2}=0,5$$

$$x=-\frac{1}{2}=-0,5$$

$$x=-\sqrt{5}i\approx -0-2,236067977i$$

$$x=\sqrt{5}i\approx 2,236067977i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$4t^{2}+19t-5=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 4 ni, b uchun 19 ni va c uchun -5 ni ayiring.

$$t=\frac{-19±\sqrt{19^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

Hisoblarni amalga oshiring.

$$t=\frac{-19±21}{8}$$

t=\frac{-19±21}{8} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{1}{4} t=-5$$

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

$$x=-\frac{1}{2} x=\frac{1}{2} x=-\sqrt{5}i x=\sqrt{5}i$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

$$x=\frac{1}{2}=0,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$4t^{2}+19t-5=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 4 ni, b uchun 19 ni va c uchun -5 ni ayiring.

$$t=\frac{-19±\sqrt{19^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

Hisoblarni amalga oshiring.

$$t=\frac{-19±21}{8}$$

t=\frac{-19±21}{8} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{1}{4} t=-5$$

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

$$x=\frac{1}{2} x=-\frac{1}{2}$$