x uchun yechish (complex solution)
x=1
x=-1
x=-\frac{3\sqrt{10}i}{10}\approx -0-0,948683298i
x=\frac{3\sqrt{10}i}{10}\approx 0,948683298i
x uchun yechish
x=-1
x=1
Grafik
Baham ko'rish
Klipbordga nusxa olish
\frac{10}{3}x^{4}-\frac{1}{3}x^{2}-3=0
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
\frac{10}{3}t^{2}-\frac{1}{3}t-3=0
x^{2} uchun t ni almashtiring.
t=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\left(-\frac{1}{3}\right)^{2}-4\times \frac{10}{3}\left(-3\right)}}{2\times \frac{10}{3}}
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun \frac{10}{3} ni, b uchun -\frac{1}{3} ni va c uchun -3 ni ayiring.
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}}
Hisoblarni amalga oshiring.
t=1 t=-\frac{9}{10}
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.
x=-1 x=1 x=-\frac{3\sqrt{10}i}{10} x=\frac{3\sqrt{10}i}{10}
x=t^{2} boʻlganda, yechimlar har bir t uchun x=±\sqrt{t} hisoblanishi orqali olinadi.
\frac{10}{3}x^{4}-\frac{1}{3}x^{2}-3=0
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
\frac{10}{3}t^{2}-\frac{1}{3}t-3=0
x^{2} uchun t ni almashtiring.
t=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\left(-\frac{1}{3}\right)^{2}-4\times \frac{10}{3}\left(-3\right)}}{2\times \frac{10}{3}}
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun \frac{10}{3} ni, b uchun -\frac{1}{3} ni va c uchun -3 ni ayiring.
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}}
Hisoblarni amalga oshiring.
t=1 t=-\frac{9}{10}
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.
x=1 x=-1
x=t^{2} boʻlganda, yechimlar musbat t uchun x=±\sqrt{t} hisoblanishi orqali olinadi.
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