y^2-y=0 eching

$$y ^ { 2 } - y = 0$$

y uchun yechish

$$y=1$$

$$y=0$$

Faktorlash qadamlari

y omili.

$$y\left(y-1\right)=0$$

Tenglamani yechish uchun y=0 va y-1=0 ni yeching.

$$y=0 y=1$$

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.

$$y^{2}-y=0$$

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 0 ni c bilan almashtiring.

$$y=\frac{-\left(-1\right)±\sqrt{1}}{2}$$

1 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-1\right)±1}{2}$$

-1 ning teskarisi 1 ga teng.

$$y=\frac{1±1}{2}$$

y=\frac{1±1}{2} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$y=\frac{2}{2}$$

2 ni 2 ga bo'lish.

$$y=1$$

y=\frac{1±1}{2} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

$$y=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$y=0$$

Tenglama yechildi.

$$y=1 y=0$$

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.

$$y^{2}-y=0$$

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$y^{2}-y+\frac{1}{4}=\frac{1}{4}$$

y^{2}-y+\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.

$$\left(y-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$y=1 y=0$$