q^2-2q+1/2=0 eching

$$q ^ { 2 } - 2 q + \frac { 1 } { 2 } = 0$$

q uchun yechish

$$q=\frac{\sqrt{2}}{2}+1\approx 1,707106781$$

$$q=-\frac{\sqrt{2}}{2}+1\approx 0,292893219$$

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.

$$q^{2}-2q+\frac{1}{2}=0$$

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

$$q=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times \frac{1}{2}}}{2}$$

-2 kvadratini chiqarish.

$$q=\frac{-\left(-2\right)±\sqrt{4-4\times \frac{1}{2}}}{2}$$

-4 ni \frac{1}{2} marotabaga ko'paytirish.

$$q=\frac{-\left(-2\right)±\sqrt{4-2}}{2}$$

4 ni -2 ga qo'shish.

$$q=\frac{-\left(-2\right)±\sqrt{2}}{2}$$

-2 ning teskarisi 2 ga teng.

$$q=\frac{2±\sqrt{2}}{2}$$

q=\frac{2±\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 2 ni \sqrt{2} ga qo'shish.

$$q=\frac{\sqrt{2}+2}{2}$$

2+\sqrt{2} ni 2 ga bo'lish.

$$q=\frac{\sqrt{2}}{2}+1$$

q=\frac{2±\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan \sqrt{2} ni ayirish.

$$q=\frac{2-\sqrt{2}}{2}$$

2-\sqrt{2} ni 2 ga bo'lish.

$$q=-\frac{\sqrt{2}}{2}+1$$

Tenglama yechildi.

$$q=\frac{\sqrt{2}}{2}+1 q=-\frac{\sqrt{2}}{2}+1$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$q^{2}-2q+\frac{1}{2}=0$$

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

$$q^{2}-2q+\frac{1}{2}-\frac{1}{2}=-\frac{1}{2}$$

O‘zidan \frac{1}{2} ayirilsa 0 qoladi.

$$q^{2}-2q=-\frac{1}{2}$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$q^{2}-2q+1=-\frac{1}{2}+1$$

-\frac{1}{2} ni 1 ga qo'shish.

$$q^{2}-2q+1=\frac{1}{2}$$

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

$$\left(q-1\right)^{2}=\frac{1}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(q-1\right)^{2}}=\sqrt{\frac{1}{2}}$$

Qisqartirish.

$$q-1=\frac{\sqrt{2}}{2} q-1=-\frac{\sqrt{2}}{2}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$q=\frac{\sqrt{2}}{2}+1 q=-\frac{\sqrt{2}}{2}+1$$