x^4-11x^2+28=0 eching

$$x ^ { 4 } - 11 x ^ { 2 } + 28 = 0$$

x uchun yechish

$$x=-\sqrt{7}\approx -2,645751311$$

$$x=\sqrt{7}\approx 2,645751311$$

$$x=2$$

$$x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$t^{2}-11t+28=0$$

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 -11 ni va c uchun 28 ni ayiring.

$$t=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 1\times 28}}{2}$$

Hisoblarni amalga oshiring.

$$t=\frac{11±3}{2}$$

t=\frac{11±3}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=7 t=4$$

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

$$x=\sqrt{7} x=-\sqrt{7} x=2 x=-2$$