3x^4+47x^2-14=0 eching

$$3 x ^ { 4 } + 47 x ^ { 2 } - 14 = 0$$

x uchun yechish (complex solution)

$$x=\frac{i\sqrt{6\left(\sqrt{2377}+47\right)}}{6}\approx 3,994881871i$$

$$x=-\frac{i\sqrt{6\left(\sqrt{2377}+47\right)}}{6}\approx -0-3,994881871i$$

$$x=-\frac{\sqrt{6\left(\sqrt{2377}-47\right)}}{6}\approx -0,540753637$$

$$x=\frac{\sqrt{6\left(\sqrt{2377}-47\right)}}{6}\approx 0,540753637$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$3t^{2}+47t-14=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 3 ni, b uchun 47 ni va c uchun -14 ni ayiring.

$$t=\frac{-47±\sqrt{47^{2}-4\times 3\left(-14\right)}}{2\times 3}$$

Hisoblarni amalga oshiring.

$$t=\frac{-47±\sqrt{2377}}{6}$$

t=\frac{-47±\sqrt{2377}}{6} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{2377}-47}{6} t=\frac{-\sqrt{2377}-47}{6}$$

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

$$x=-\sqrt{\frac{\sqrt{2377}-47}{6}} x=\sqrt{\frac{\sqrt{2377}-47}{6}} x=-i\sqrt{\frac{\sqrt{2377}+47}{6}} x=i\sqrt{\frac{\sqrt{2377}+47}{6}}$$

x uchun yechish

$$x=-\frac{\sqrt{6\left(\sqrt{2377}-47\right)}}{6}\approx -0,540753637$$

$$x=\frac{\sqrt{6\left(\sqrt{2377}-47\right)}}{6}\approx 0,540753637$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$3t^{2}+47t-14=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 3 ni, b uchun 47 ni va c uchun -14 ni ayiring.

$$t=\frac{-47±\sqrt{47^{2}-4\times 3\left(-14\right)}}{2\times 3}$$

Hisoblarni amalga oshiring.

$$t=\frac{-47±\sqrt{2377}}{6}$$

t=\frac{-47±\sqrt{2377}}{6} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{\sqrt{2377}-47}{6} t=\frac{-\sqrt{2377}-47}{6}$$

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

$$x=\frac{\sqrt{\frac{2\sqrt{2377}-94}{3}}}{2} x=-\frac{\sqrt{\frac{2\sqrt{2377}-94}{3}}}{2}$$