16b^2-25=0 eching

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

b uchun yechish

$$b = \frac{5}{4} = 1\frac{1}{4} = 1,25$$

$$b = -\frac{5}{4} = -1\frac{1}{4} = -1,25$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 16b^{2}-25. 16b^{2}-25 ni \left(4b\right)^{2}-5^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

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

Kvadrat ildizini topish bo'yicha qadamlar

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

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

Ikki tarafini 16 ga bo‘ling.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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.

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

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 -25 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 16 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{-64\left(-25\right)}}{2\times 16}$$

-64 ni -25 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{1600}}{2\times 16}$$

1600 ning kvadrat ildizini chiqarish.

$$b=\frac{0±40}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$b=\frac{0±40}{32}$$

b=\frac{0±40}{32} tenglamasini yeching, bunda ± musbat. \frac{40}{32} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

b=\frac{0±40}{32} tenglamasini yeching, bunda ± manfiy. \frac{-40}{32} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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