4b^2-121=0 eching

$$4 b ^ { 2 } - 121 = 0$$

b uchun yechish

$$b = \frac{11}{2} = 5\frac{1}{2} = 5,5$$

$$b = -\frac{11}{2} = -5\frac{1}{2} = -5,5$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 4b^{2}-121. 4b^{2}-121 ni \left(2b\right)^{2}-11^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2b-11\right)\left(2b+11\right)=0$$

Tenglamani yechish uchun 2b-11=0 va 2b+11=0 ni yeching.

$$b=\frac{11}{2} b=-\frac{11}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$4b^{2}=121$$

Ikki tarafini 4 ga bo‘ling.

$$b^{2}=\frac{121}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$b=\frac{11}{2} b=-\frac{11}{2}$$

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.

$$4b^{2}-121=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va -121 ni c bilan almashtiring.

$$b=\frac{0±\sqrt{0^{2}-4\times 4\left(-121\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$b=\frac{0±\sqrt{-4\times 4\left(-121\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{-16\left(-121\right)}}{2\times 4}$$

-16 ni -121 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{1936}}{2\times 4}$$

1936 ning kvadrat ildizini chiqarish.

$$b=\frac{0±44}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$b=\frac{0±44}{8}$$

b=\frac{0±44}{8} tenglamasini yeching, bunda ± musbat. \frac{44}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=\frac{11}{2}$$

b=\frac{0±44}{8} tenglamasini yeching, bunda ± manfiy. \frac{-44}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=-\frac{11}{2}$$

Tenglama yechildi.

$$b=\frac{11}{2} b=-\frac{11}{2}$$