-x^2(x^2-13)=-42 eching

$$- x ^ { 2 } ( x ^ { 2 } - 13 ) = - 42$$

x uchun yechish (complex solution)

$$x=\frac{i\sqrt{2\left(\sqrt{337}-13\right)}}{2}\approx 1,636697857i$$

$$x=-\frac{i\sqrt{2\left(\sqrt{337}-13\right)}}{2}\approx -0-1,636697857i$$

$$x = -\frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx -3,959643908$$

$$x = \frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx 3,959643908$$

Kvadrat tenglamalaridan foydalanish qoidalari

-x^{2} ga x^{2}-13 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x^{2}\right)x^{2}-13\left(-x^{2}\right)=-42$$

13 hosil qilish uchun -13 va -1 ni ko'paytirish.

$$\left(-x^{2}\right)x^{2}+13x^{2}=-42$$

42 ni ikki tarafga qo’shing.

$$\left(-x^{2}\right)x^{2}+13x^{2}+42=0$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

$$-x^{4}+13x^{2}+42=0$$

x^{2} uchun t ni almashtiring.

$$-t^{2}+13t+42=0$$

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 13 ni va c uchun 42 ni ayiring.

$$t=\frac{-13±\sqrt{13^{2}-4\left(-1\right)\times 42}}{-2}$$

Hisoblarni amalga oshiring.

$$t=\frac{-13±\sqrt{337}}{-2}$$

t=\frac{-13±\sqrt{337}}{-2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{13-\sqrt{337}}{2} t=\frac{\sqrt{337}+13}{2}$$

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

$$x=-i\sqrt{-\frac{13-\sqrt{337}}{2}} x=i\sqrt{-\frac{13-\sqrt{337}}{2}} x=-\sqrt{\frac{\sqrt{337}+13}{2}} x=\sqrt{\frac{\sqrt{337}+13}{2}}$$

x uchun yechish

$$x = -\frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx -3,959643908$$

$$x = \frac{\sqrt{2 {(\sqrt{337} + 13)}}}{2} \approx 3,959643908$$

Kvadrat tenglamalaridan foydalanish qoidalari

-x^{2} ga x^{2}-13 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x^{2}\right)x^{2}-13\left(-x^{2}\right)=-42$$

13 hosil qilish uchun -13 va -1 ni ko'paytirish.

$$\left(-x^{2}\right)x^{2}+13x^{2}=-42$$

42 ni ikki tarafga qo’shing.

$$\left(-x^{2}\right)x^{2}+13x^{2}+42=0$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 2 ni qo‘shib, 4 ni oling.

$$-x^{4}+13x^{2}+42=0$$

x^{2} uchun t ni almashtiring.

$$-t^{2}+13t+42=0$$

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 13 ni va c uchun 42 ni ayiring.

$$t=\frac{-13±\sqrt{13^{2}-4\left(-1\right)\times 42}}{-2}$$

Hisoblarni amalga oshiring.

$$t=\frac{-13±\sqrt{337}}{-2}$$

t=\frac{-13±\sqrt{337}}{-2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{13-\sqrt{337}}{2} t=\frac{\sqrt{337}+13}{2}$$

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

$$x=\frac{\sqrt{2\sqrt{337}+26}}{2} x=-\frac{\sqrt{2\sqrt{337}+26}}{2}$$