x^4+4/x^4=4 eching

$$x ^ { 4 } + \frac { 4 } { x ^ { 4 } } = 4$$

x uchun yechish (complex solution)

$$x=\sqrt[4]{2}i\approx 1,189207115i$$

$$x=\sqrt[4]{2}\approx 1,189207115$$

$$x=-\sqrt[4]{2}\approx -1,189207115$$

$$x=-\sqrt[4]{2}i\approx -0-1,189207115i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{4} ga ko'paytirish.

$$x^{4}x^{4}+4=4x^{4}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 4 ni qo‘shib, 8 ni oling.

$$x^{8}+4=4x^{4}$$

Ikkala tarafdan 4x^{4} ni ayirish.

$$x^{8}+4-4x^{4}=0$$

x^{4} uchun t ni almashtiring.

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

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 -4 ni va c uchun 4 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{4±0}{2}$$

Yechimlar bir xil.

$$t=2$$

x=t^{4} boʻlganda, yechimlar har bir t uchun tenglamani yechish orqali olinadi.

$$x=\sqrt[4]{2} x=\sqrt[4]{2}i x=-\sqrt[4]{2} x=-\sqrt[4]{2}i$$

x uchun yechish

$$x=\sqrt[4]{2}\approx 1,189207115$$

$$x=-\sqrt[4]{2}\approx -1,189207115$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{4} ga ko'paytirish.

$$x^{4}x^{4}+4=4x^{4}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 4 ni qo‘shib, 8 ni oling.

$$x^{8}+4=4x^{4}$$

Ikkala tarafdan 4x^{4} ni ayirish.

$$x^{8}+4-4x^{4}=0$$

x^{4} uchun t ni almashtiring.

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

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 -4 ni va c uchun 4 ni ayiring.

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

Hisoblarni amalga oshiring.

$$t=\frac{4±0}{2}$$

Yechimlar bir xil.

$$t=2$$

x=t^{4} boʻlganda, yechimlar musbat t uchun x=±\sqrt[4]{t} hisoblanishi orqali olinadi.

$$x=-\sqrt[4]{2} x=\sqrt[4]{2}$$