25w^2-16=0 eching

$$25 w ^ { 2 } - 16 = 0$$

w uchun yechish

$$w=\frac{4}{5}=0,8$$

$$w=-\frac{4}{5}=-0,8$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 25w^{2}-16. 25w^{2}-16 ni \left(5w\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).

$$\left(5w-4\right)\left(5w+4\right)=0$$

Tenglamani yechish uchun 5w-4=0 va 5w+4=0 ni yeching.

$$w=\frac{4}{5} w=-\frac{4}{5}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$25w^{2}=16$$

Ikki tarafini 25 ga bo‘ling.

$$w^{2}=\frac{16}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$w=\frac{4}{5} w=-\frac{4}{5}$$

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.

$$25w^{2}-16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 25 ni a, 0 ni b va -16 ni c bilan almashtiring.

$$w=\frac{0±\sqrt{0^{2}-4\times 25\left(-16\right)}}{2\times 25}$$

0 kvadratini chiqarish.

$$w=\frac{0±\sqrt{-4\times 25\left(-16\right)}}{2\times 25}$$

-4 ni 25 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{-100\left(-16\right)}}{2\times 25}$$

-100 ni -16 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{1600}}{2\times 25}$$

1600 ning kvadrat ildizini chiqarish.

$$w=\frac{0±40}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$w=\frac{0±40}{50}$$

w=\frac{0±40}{50} tenglamasini yeching, bunda ± musbat. \frac{40}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=\frac{4}{5}$$

w=\frac{0±40}{50} tenglamasini yeching, bunda ± manfiy. \frac{-40}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=-\frac{4}{5}$$

Tenglama yechildi.

$$w=\frac{4}{5} w=-\frac{4}{5}$$