b^2+b+1/4=0 eching

$$b ^ { 2 } + b + \frac { 1 } { 4 } = 0$$

b uchun yechish

$$b=-\frac{1}{2}=-0,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$b^{2}+b+\frac{1}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1 ni b va \frac{1}{4} ni c bilan almashtiring.

$$b=\frac{-1±\sqrt{1^{2}-4\times \frac{1}{4}}}{2}$$

1 kvadratini chiqarish.

$$b=\frac{-1±\sqrt{1-4\times \frac{1}{4}}}{2}$$

-4 ni \frac{1}{4} marotabaga ko'paytirish.

$$b=\frac{-1±\sqrt{1-1}}{2}$$

1 ni -1 ga qo'shish.

$$b=\frac{-1±\sqrt{0}}{2}$$

0 ning kvadrat ildizini chiqarish.

$$b=-\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

b^{2}+b+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(b+\frac{1}{2}\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b+\frac{1}{2}\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$b+\frac{1}{2}=0 b+\frac{1}{2}=0$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$b=-\frac{1}{2} b=-\frac{1}{2}$$

Tenglama yechildi. Yechimlar bir xil.

$$b=-\frac{1}{2}$$