x^4+34x^2+225=0 eching

$$x ^ { 4 } + 34 x ^ { 2 } + 225 = 0$$

x uchun yechish (complex solution)

$$x=3i$$

$$x=-3i$$

$$x=-5i$$

$$x=5i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}+34t+225=0$$

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 34 ni va c uchun 225 ni ayiring.

$$t=\frac{-34±\sqrt{34^{2}-4\times 1\times 225}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{-34±16}{2}$$

t=\frac{-34±16}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=-9 t=-25$$

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

$$x=-3i x=3i x=-5i x=5i$$