3k^2-8=-5 eching

$$3 k ^ { 2 } - 8 = - 5$$

k uchun yechish

$$k=1$$

$$k=-1$$

Kvadratlar farqidan foydalangan qadamlar

5 ni ikki tarafga qo’shing.

$$3k^{2}-8+5=0$$

-3 olish uchun -8 va 5'ni qo'shing.

$$3k^{2}-3=0$$

Ikki tarafini 3 ga bo‘ling.

$$k^{2}-1=0$$

Hisoblang: k^{2}-1. k^{2}-1 ni k^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(k-1\right)\left(k+1\right)=0$$

Tenglamani yechish uchun k-1=0 va k+1=0 ni yeching.

$$k=1 k=-1$$

Kvadrat ildizini topish bo'yicha qadamlar

8 ni ikki tarafga qo’shing.

$$3k^{2}=-5+8$$

3 olish uchun -5 va 8'ni qo'shing.

$$3k^{2}=3$$

Ikki tarafini 3 ga bo‘ling.

$$k^{2}=\frac{3}{3}$$

1 ni olish uchun 3 ni 3 ga bo‘ling.

$$k^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$k=1 k=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

5 ni ikki tarafga qo’shing.

$$3k^{2}-8+5=0$$

-3 olish uchun -8 va 5'ni qo'shing.

$$3k^{2}-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -3 ni c bilan almashtiring.

$$k=\frac{0±\sqrt{0^{2}-4\times 3\left(-3\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$k=\frac{0±\sqrt{-4\times 3\left(-3\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{-12\left(-3\right)}}{2\times 3}$$

-12 ni -3 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{36}}{2\times 3}$$

36 ning kvadrat ildizini chiqarish.

$$k=\frac{0±6}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$k=\frac{0±6}{6}$$

k=\frac{0±6}{6} tenglamasini yeching, bunda ± musbat. 6 ni 6 ga bo'lish.

$$k=1$$

k=\frac{0±6}{6} tenglamasini yeching, bunda ± manfiy. -6 ni 6 ga bo'lish.

$$k=-1$$

Tenglama yechildi.

$$k=1 k=-1$$