y^2-6y+25=0 eching

$${ y }^{ 2 } -6y+25=0$$

y uchun yechish

$$y=3+4i$$

$$y=3-4i$$

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.

$$y^{2}-6y+25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va 25 ni c bilan almashtiring.

$$y=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 25}}{2}$$

-6 kvadratini chiqarish.

$$y=\frac{-\left(-6\right)±\sqrt{36-4\times 25}}{2}$$

-4 ni 25 marotabaga ko'paytirish.

$$y=\frac{-\left(-6\right)±\sqrt{36-100}}{2}$$

36 ni -100 ga qo'shish.

$$y=\frac{-\left(-6\right)±\sqrt{-64}}{2}$$

-64 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-6\right)±8i}{2}$$

-6 ning teskarisi 6 ga teng.

$$y=\frac{6±8i}{2}$$

y=\frac{6±8i}{2} tenglamasini yeching, bunda ± musbat. 6 ni 8i ga qo'shish.

$$y=\frac{6+8i}{2}$$

6+8i ni 2 ga bo'lish.

$$y=3+4i$$

y=\frac{6±8i}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 8i ni ayirish.

$$y=\frac{6-8i}{2}$$

6-8i ni 2 ga bo'lish.

$$y=3-4i$$

Tenglama yechildi.

$$y=3+4i y=3-4i$$

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.

$$y^{2}-6y+25=0$$

Tenglamaning ikkala tarafidan 25 ni ayirish.

$$y^{2}-6y+25-25=-25$$

O‘zidan 25 ayirilsa 0 qoladi.

$$y^{2}-6y=-25$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-6y+\left(-3\right)^{2}=-25+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$y^{2}-6y+9=-25+9$$

-25 ni 9 ga qo'shish.

$$y^{2}-6y+9=-16$$

y^{2}-6y+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-3\right)^{2}=-16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-3\right)^{2}}=\sqrt{-16}$$

Qisqartirish.

$$y-3=4i y-3=-4i$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$y=3+4i y=3-4i$$