6x^4-7x^2+2=0 eching

$$6 x ^ { 4 } - 7 x ^ { 2 } + 2 = 0$$

x uchun yechish

$$x=-\frac{\sqrt{6}}{3}\approx -0,816496581$$

$$x=\frac{\sqrt{6}}{3}\approx 0,816496581$$

$$x=\frac{\sqrt{2}}{2}\approx 0,707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0,707106781$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} uchun t ni almashtiring.

$$6t^{2}-7t+2=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 6 ni, b uchun -7 ni va c uchun 2 ni ayiring.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6\times 2}}{2\times 6}$$

Hisoblarni amalga oshiring.

$$t=\frac{7±1}{12}$$

t=\frac{7±1}{12} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{2}{3} t=\frac{1}{2}$$

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

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3} x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2}$$