3/x^4-1-1/2x^2+2=-1/6-6x^2 eching

$$\frac { 3 } { x ^ { 4 } - 1 } - \frac { 1 } { 2 x ^ { 2 } + 2 } = - \frac { 1 } { 6 - 6 x ^ { 2 } }$$

x uchun yechish

$$x=\sqrt{5}\approx 2,236067977$$

$$x=-\sqrt{5}\approx -2,236067977$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right) ga, x^{4}-1,2x^{2}+2,6-6x^{2} ning eng kichik karralisiga ko‘paytiring.

$$6\times 3-\left(3x^{2}-3\right)=1+x^{2}$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$18-\left(3x^{2}-3\right)=1+x^{2}$$

3x^{2}-3 teskarisini topish uchun har birining teskarisini toping.

$$18-3x^{2}+3=1+x^{2}$$

21 olish uchun 18 va 3'ni qo'shing.

$$21-3x^{2}=1+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$21-3x^{2}-x^{2}=1$$

-4x^{2} ni olish uchun -3x^{2} va -x^{2} ni birlashtirish.

$$21-4x^{2}=1$$

Ikkala tarafdan 21 ni ayirish.

$$-4x^{2}=1-21$$

-20 olish uchun 1 dan 21 ni ayirish.

$$-4x^{2}=-20$$

Ikki tarafini -4 ga bo‘ling.

$$x^{2}=\frac{-20}{-4}$$

5 ni olish uchun -20 ni -4 ga bo‘ling.

$$x^{2}=5$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{5} x=-\sqrt{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right) ga, x^{4}-1,2x^{2}+2,6-6x^{2} ning eng kichik karralisiga ko‘paytiring.

$$6\times 3-\left(3x^{2}-3\right)=1+x^{2}$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$18-\left(3x^{2}-3\right)=1+x^{2}$$

3x^{2}-3 teskarisini topish uchun har birining teskarisini toping.

$$18-3x^{2}+3=1+x^{2}$$

21 olish uchun 18 va 3'ni qo'shing.

$$21-3x^{2}=1+x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$21-3x^{2}-1=x^{2}$$

20 olish uchun 21 dan 1 ni ayirish.

$$20-3x^{2}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$20-3x^{2}-x^{2}=0$$

-4x^{2} ni olish uchun -3x^{2} va -x^{2} ni birlashtirish.

$$20-4x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-4x^{2}+20=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -4 ni a, 0 ni b va 20 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 20}}{2\left(-4\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 20}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16\times 20}}{2\left(-4\right)}$$

16 ni 20 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{320}}{2\left(-4\right)}$$

320 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{5}}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{5}}{-8}$$

x=\frac{0±8\sqrt{5}}{-8} tenglamasini yeching, bunda ± musbat.

$$x=-\sqrt{5}$$

x=\frac{0±8\sqrt{5}}{-8} tenglamasini yeching, bunda ± manfiy.

$$x=\sqrt{5}$$

Tenglama yechildi.

$$x=-\sqrt{5} x=\sqrt{5}$$