(4k)^2-4(6)(k^2-1)=0 eching

$$( 4 k ) ^ { 2 } - 4 ( 6 ) ( k ^ { 2 } - 1 ) = 0$$

k uchun yechish

$$k=\sqrt{3}\approx 1,732050808$$

$$k=-\sqrt{3}\approx -1,732050808$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(4k\right)^{2} ni kengaytirish.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

-24 ga k^{2}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16k^{2}-24k^{2}+24=0$$

-8k^{2} ni olish uchun 16k^{2} va -24k^{2} ni birlashtirish.

$$-8k^{2}+24=0$$

Ikkala tarafdan 24 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-8k^{2}=-24$$

Ikki tarafini -8 ga bo‘ling.

$$k^{2}=\frac{-24}{-8}$$

3 ni olish uchun -24 ni -8 ga bo‘ling.

$$k^{2}=3$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$k=\sqrt{3} k=-\sqrt{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(4k\right)^{2} ni kengaytirish.

$$4^{2}k^{2}-4\times 6\left(k^{2}-1\right)=0$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16k^{2}-4\times 6\left(k^{2}-1\right)=0$$

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$16k^{2}-24\left(k^{2}-1\right)=0$$

-24 ga k^{2}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16k^{2}-24k^{2}+24=0$$

-8k^{2} ni olish uchun 16k^{2} va -24k^{2} ni birlashtirish.

$$-8k^{2}+24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -8 ni a, 0 ni b va 24 ni c bilan almashtiring.

$$k=\frac{0±\sqrt{0^{2}-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

0 kvadratini chiqarish.

$$k=\frac{0±\sqrt{-4\left(-8\right)\times 24}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{32\times 24}}{2\left(-8\right)}$$

32 ni 24 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{768}}{2\left(-8\right)}$$

768 ning kvadrat ildizini chiqarish.

$$k=\frac{0±16\sqrt{3}}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$k=\frac{0±16\sqrt{3}}{-16}$$

k=\frac{0±16\sqrt{3}}{-16} tenglamasini yeching, bunda ± musbat.

$$k=-\sqrt{3}$$

k=\frac{0±16\sqrt{3}}{-16} tenglamasini yeching, bunda ± manfiy.

$$k=\sqrt{3}$$

Tenglama yechildi.

$$k=-\sqrt{3} k=\sqrt{3}$$