5a^2-a-5a+1=12a^2-5a-6a eching

$$5 a ^ { 2 } - a - 5 a + 1 = 12 a ^ { 2 } - 5 a - 6 a$$

a uchun yechish

$$a=\frac{\sqrt{53}+5}{14}\approx 0,877150706$$

$$a=\frac{5-\sqrt{53}}{14}\approx -0,162864992$$

Kvadrat tenglamalaridan foydalanish qoidalari

-6a ni olish uchun -a va -5a ni birlashtirish.

$$5a^{2}-6a+1=12a^{2}-5a-6a$$

-11a ni olish uchun -5a va -6a ni birlashtirish.

$$5a^{2}-6a+1=12a^{2}-11a$$

Ikkala tarafdan 12a^{2} ni ayirish.

$$5a^{2}-6a+1-12a^{2}=-11a$$

-7a^{2} ni olish uchun 5a^{2} va -12a^{2} ni birlashtirish.

$$-7a^{2}-6a+1=-11a$$

11a ni ikki tarafga qo’shing.

$$-7a^{2}-6a+1+11a=0$$

5a ni olish uchun -6a va 11a ni birlashtirish.

$$-7a^{2}+5a+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -7 ni a, 5 ni b va 1 ni c bilan almashtiring.

$$a=\frac{-5±\sqrt{5^{2}-4\left(-7\right)}}{2\left(-7\right)}$$

5 kvadratini chiqarish.

$$a=\frac{-5±\sqrt{25-4\left(-7\right)}}{2\left(-7\right)}$$

-4 ni -7 marotabaga ko'paytirish.

$$a=\frac{-5±\sqrt{25+28}}{2\left(-7\right)}$$

25 ni 28 ga qo'shish.

$$a=\frac{-5±\sqrt{53}}{2\left(-7\right)}$$

2 ni -7 marotabaga ko'paytirish.

$$a=\frac{-5±\sqrt{53}}{-14}$$

a=\frac{-5±\sqrt{53}}{-14} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{53} ga qo'shish.

$$a=\frac{\sqrt{53}-5}{-14}$$

-5+\sqrt{53} ni -14 ga bo'lish.

$$a=\frac{5-\sqrt{53}}{14}$$

a=\frac{-5±\sqrt{53}}{-14} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{53} ni ayirish.

$$a=\frac{-\sqrt{53}-5}{-14}$$

-5-\sqrt{53} ni -14 ga bo'lish.

$$a=\frac{\sqrt{53}+5}{14}$$

Tenglama yechildi.

$$a=\frac{5-\sqrt{53}}{14} a=\frac{\sqrt{53}+5}{14}$$

Kvadratni yakunlash bo'yicha qadamlar

-6a ni olish uchun -a va -5a ni birlashtirish.

$$5a^{2}-6a+1=12a^{2}-5a-6a$$

-11a ni olish uchun -5a va -6a ni birlashtirish.

$$5a^{2}-6a+1=12a^{2}-11a$$

Ikkala tarafdan 12a^{2} ni ayirish.

$$5a^{2}-6a+1-12a^{2}=-11a$$

-7a^{2} ni olish uchun 5a^{2} va -12a^{2} ni birlashtirish.

$$-7a^{2}-6a+1=-11a$$

11a ni ikki tarafga qo’shing.

$$-7a^{2}-6a+1+11a=0$$

5a ni olish uchun -6a va 11a ni birlashtirish.

$$-7a^{2}+5a+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-7a^{2}+5a=-1$$

Ikki tarafini -7 ga bo‘ling.

$$\frac{-7a^{2}+5a}{-7}=-\frac{1}{-7}$$

-7 ga bo'lish -7 ga ko'paytirishni bekor qiladi.

$$a^{2}+\frac{5}{-7}a=-\frac{1}{-7}$$

5 ni -7 ga bo'lish.

$$a^{2}-\frac{5}{7}a=-\frac{1}{-7}$$

-1 ni -7 ga bo'lish.

$$a^{2}-\frac{5}{7}a=\frac{1}{7}$$

-\frac{5}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{14} olish uchun. Keyin, -\frac{5}{14} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-\frac{5}{7}a+\left(-\frac{5}{14}\right)^{2}=\frac{1}{7}+\left(-\frac{5}{14}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{14} kvadratini chiqarish.

$$a^{2}-\frac{5}{7}a+\frac{25}{196}=\frac{1}{7}+\frac{25}{196}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{7} ni \frac{25}{196} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$a^{2}-\frac{5}{7}a+\frac{25}{196}=\frac{53}{196}$$

a^{2}-\frac{5}{7}a+\frac{25}{196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a-\frac{5}{14}\right)^{2}=\frac{53}{196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-\frac{5}{14}\right)^{2}}=\sqrt{\frac{53}{196}}$$

Qisqartirish.

$$a-\frac{5}{14}=\frac{\sqrt{53}}{14} a-\frac{5}{14}=-\frac{\sqrt{53}}{14}$$

\frac{5}{14} ni tenglamaning ikkala tarafiga qo'shish.

$$a=\frac{\sqrt{53}+5}{14} a=\frac{5-\sqrt{53}}{14}$$