16k^2-144=0 eching

$$16 k ^ { 2 } - 144 = 0$$

k uchun yechish

$$k=3$$

$$k=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 16 ga bo‘ling.

$$k^{2}-9=0$$

Hisoblang: k^{2}-9. k^{2}-9 ni k^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(k-3\right)\left(k+3\right)=0$$

Tenglamani yechish uchun k-3=0 va k+3=0 ni yeching.

$$k=3 k=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$16k^{2}=144$$

Ikki tarafini 16 ga bo‘ling.

$$k^{2}=\frac{144}{16}$$

9 ni olish uchun 144 ni 16 ga bo‘ling.

$$k^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$k=3 k=-3$$

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.

$$16k^{2}-144=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, 0 ni b va -144 ni c bilan almashtiring.

$$k=\frac{0±\sqrt{0^{2}-4\times 16\left(-144\right)}}{2\times 16}$$

0 kvadratini chiqarish.

$$k=\frac{0±\sqrt{-4\times 16\left(-144\right)}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{-64\left(-144\right)}}{2\times 16}$$

-64 ni -144 marotabaga ko'paytirish.

$$k=\frac{0±\sqrt{9216}}{2\times 16}$$

9216 ning kvadrat ildizini chiqarish.

$$k=\frac{0±96}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$k=\frac{0±96}{32}$$

k=\frac{0±96}{32} tenglamasini yeching, bunda ± musbat. 96 ni 32 ga bo'lish.

$$k=3$$

k=\frac{0±96}{32} tenglamasini yeching, bunda ± manfiy. -96 ni 32 ga bo'lish.

$$k=-3$$

Tenglama yechildi.

$$k=3 k=-3$$