d(10d-9)+1=0 eching

$$d ( 10 d - 9 ) + 1 = 0$$

d uchun yechish

$$d=\frac{\sqrt{41}+9}{20}\approx 0,770156212$$

$$d=\frac{9-\sqrt{41}}{20}\approx 0,129843788$$

Kvadrat tenglamalaridan foydalanish qoidalari

d ga 10d-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10d^{2}-9d+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, -9 ni b va 1 ni c bilan almashtiring.

$$d=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 10}}{2\times 10}$$

-9 kvadratini chiqarish.

$$d=\frac{-\left(-9\right)±\sqrt{81-4\times 10}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$d=\frac{-\left(-9\right)±\sqrt{81-40}}{2\times 10}$$

81 ni -40 ga qo'shish.

$$d=\frac{-\left(-9\right)±\sqrt{41}}{2\times 10}$$

-9 ning teskarisi 9 ga teng.

$$d=\frac{9±\sqrt{41}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$d=\frac{9±\sqrt{41}}{20}$$

d=\frac{9±\sqrt{41}}{20} tenglamasini yeching, bunda ± musbat. 9 ni \sqrt{41} ga qo'shish.

$$d=\frac{\sqrt{41}+9}{20}$$

d=\frac{9±\sqrt{41}}{20} tenglamasini yeching, bunda ± manfiy. 9 dan \sqrt{41} ni ayirish.

$$d=\frac{9-\sqrt{41}}{20}$$

Tenglama yechildi.

$$d=\frac{\sqrt{41}+9}{20} d=\frac{9-\sqrt{41}}{20}$$

Kvadratni yakunlash bo'yicha qadamlar

d ga 10d-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10d^{2}-9d+1=0$$

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

$$10d^{2}-9d=-1$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10d^{2}-9d}{10}=-\frac{1}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$d^{2}-\frac{9}{10}d=-\frac{1}{10}$$

-\frac{9}{10} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{20} olish uchun. Keyin, -\frac{9}{20} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$d^{2}-\frac{9}{10}d+\left(-\frac{9}{20}\right)^{2}=-\frac{1}{10}+\left(-\frac{9}{20}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{20} kvadratini chiqarish.

$$d^{2}-\frac{9}{10}d+\frac{81}{400}=-\frac{1}{10}+\frac{81}{400}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{10} ni \frac{81}{400} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$d^{2}-\frac{9}{10}d+\frac{81}{400}=\frac{41}{400}$$

d^{2}-\frac{9}{10}d+\frac{81}{400} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(d-\frac{9}{20}\right)^{2}=\frac{41}{400}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(d-\frac{9}{20}\right)^{2}}=\sqrt{\frac{41}{400}}$$

Qisqartirish.

$$d-\frac{9}{20}=\frac{\sqrt{41}}{20} d-\frac{9}{20}=-\frac{\sqrt{41}}{20}$$

\frac{9}{20} ni tenglamaning ikkala tarafiga qo'shish.

$$d=\frac{\sqrt{41}+9}{20} d=\frac{9-\sqrt{41}}{20}$$