x^4-7x^2+12=0 eching

$$x ^ { 4 } - 7 x ^ { 2 } + 12 = 0$$

x uchun yechish

$$x=-2$$

$$x=2$$

$$x=\sqrt{3}\approx 1,732050808$$

$$x=-\sqrt{3}\approx -1,732050808$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-7t+12=0$$

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 -7 ni va c uchun 12 ni ayiring.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\times 12}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{7±1}{2}$$

t=\frac{7±1}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=4 t=3$$

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

$$x=2 x=-2 x=\sqrt{3} x=-\sqrt{3}$$