5k^2-5=0 eching

$$5 k ^ { 2 } - 5 = 0$$

k uchun yechish

$$k=1$$

$$k=-1$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 5 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

5 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$5k^{2}=5$$

Ikki tarafini 5 ga bo‘ling.

$$k^{2}=\frac{5}{5}$$

1 ni olish uchun 5 ni 5 ga bo‘ling.

$$k^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$k=1 k=-1$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$5k^{2}-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -5 ni c bilan almashtiring.

$$k=\frac{0±\sqrt{0^{2}-4\times 5\left(-5\right)}}{2\times 5}$$

0 kvadratini chiqarish.

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

-4 ni 5 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{-20\left(-5\right)}}{2\times 5}$$

-20 ni -5 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{100}}{2\times 5}$$

100 ning kvadrat ildizini chiqarish.

$$k=\frac{0±10}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$k=\frac{0±10}{10}$$

k=\frac{0±10}{10} tenglamasini yeching, bunda ± musbat. 10 ni 10 ga bo'lish.

$$k=1$$

k=\frac{0±10}{10} tenglamasini yeching, bunda ± manfiy. -10 ni 10 ga bo'lish.

$$k=-1$$

Tenglama yechildi.

$$k=1 k=-1$$