81c^2-16=0 eching

$$81 c ^ { 2 } - 16 = 0$$

c uchun yechish

$$c=\frac{4}{9}\approx 0,444444444$$

$$c=-\frac{4}{9}\approx -0,444444444$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 81c^{2}-16. 81c^{2}-16 ni \left(9c\right)^{2}-4^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9c-4\right)\left(9c+4\right)=0$$

Tenglamani yechish uchun 9c-4=0 va 9c+4=0 ni yeching.

$$c=\frac{4}{9} c=-\frac{4}{9}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$81c^{2}=16$$

Ikki tarafini 81 ga bo‘ling.

$$c^{2}=\frac{16}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$c=\frac{4}{9} c=-\frac{4}{9}$$

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.

$$81c^{2}-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 81 ni a, 0 ni b va -16 ni c bilan almashtiring.

$$c=\frac{0±\sqrt{0^{2}-4\times 81\left(-16\right)}}{2\times 81}$$

0 kvadratini chiqarish.

$$c=\frac{0±\sqrt{-4\times 81\left(-16\right)}}{2\times 81}$$

-4 ni 81 marotabaga ko'paytirish.

$$c=\frac{0±\sqrt{-324\left(-16\right)}}{2\times 81}$$

-324 ni -16 marotabaga ko'paytirish.

$$c=\frac{0±\sqrt{5184}}{2\times 81}$$

5184 ning kvadrat ildizini chiqarish.

$$c=\frac{0±72}{2\times 81}$$

2 ni 81 marotabaga ko'paytirish.

$$c=\frac{0±72}{162}$$

c=\frac{0±72}{162} tenglamasini yeching, bunda ± musbat. \frac{72}{162} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$c=\frac{4}{9}$$

c=\frac{0±72}{162} tenglamasini yeching, bunda ± manfiy. \frac{-72}{162} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$c=-\frac{4}{9}$$

Tenglama yechildi.

$$c=\frac{4}{9} c=-\frac{4}{9}$$