4y^4+7y^2-36=0 eching

$$4 y ^ { 4 } + 7 y ^ { 2 } - 36 = 0$$

y uchun yechish (complex solution)

$$y = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

$$y=-2i$$

$$y=2i$$

Kvadrat tenglamalaridan foydalanish qoidalari

y^{2} uchun t ni almashtiring.

$$4t^{2}+7t-36=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 4 ni, b uchun 7 ni va c uchun -36 ni ayiring.

$$t=\frac{-7±\sqrt{7^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Hisoblarni amalga oshiring.

$$t=\frac{-7±25}{8}$$

t=\frac{-7±25}{8} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{9}{4} t=-4$$

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

$$y=-\frac{3}{2} y=\frac{3}{2} y=-2i y=2i$$

y uchun yechish

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

$$y = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

y^{2} uchun t ni almashtiring.

$$4t^{2}+7t-36=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 4 ni, b uchun 7 ni va c uchun -36 ni ayiring.

$$t=\frac{-7±\sqrt{7^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Hisoblarni amalga oshiring.

$$t=\frac{-7±25}{8}$$

t=\frac{-7±25}{8} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{9}{4} t=-4$$

y=t^{2} boʻlganda, yechimlar musbat t uchun y=±\sqrt{t} hisoblanishi orqali olinadi.

$$y=\frac{3}{2} y=-\frac{3}{2}$$