90*(x-10)*(x-9)=1 eching

$$90 \times (x-10) \times (x-9)=1$$

x uchun yechish

$$x=\frac{\sqrt{235}}{30}+\frac{19}{2}\approx 10,010990324$$

$$x=-\frac{\sqrt{235}}{30}+\frac{19}{2}\approx 8,989009676$$

Kvadrat tenglamalaridan foydalanish qoidalari

90 ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(90x-900\right)\left(x-9\right)=1$$

90x-900 ga x-9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$90x^{2}-1710x+8100=1$$

Ikkala tarafdan 1 ni ayirish.

$$90x^{2}-1710x+8100-1=0$$

8099 olish uchun 8100 dan 1 ni ayirish.

$$90x^{2}-1710x+8099=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 90 ni a, -1710 ni b va 8099 ni c bilan almashtiring.

$$x=\frac{-\left(-1710\right)±\sqrt{\left(-1710\right)^{2}-4\times 90\times 8099}}{2\times 90}$$

-1710 kvadratini chiqarish.

$$x=\frac{-\left(-1710\right)±\sqrt{2924100-4\times 90\times 8099}}{2\times 90}$$

-4 ni 90 marotabaga ko'paytirish.

$$x=\frac{-\left(-1710\right)±\sqrt{2924100-360\times 8099}}{2\times 90}$$

-360 ni 8099 marotabaga ko'paytirish.

$$x=\frac{-\left(-1710\right)±\sqrt{2924100-2915640}}{2\times 90}$$

2924100 ni -2915640 ga qo'shish.

$$x=\frac{-\left(-1710\right)±\sqrt{8460}}{2\times 90}$$

8460 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1710\right)±6\sqrt{235}}{2\times 90}$$

-1710 ning teskarisi 1710 ga teng.

$$x=\frac{1710±6\sqrt{235}}{2\times 90}$$

2 ni 90 marotabaga ko'paytirish.

$$x=\frac{1710±6\sqrt{235}}{180}$$

x=\frac{1710±6\sqrt{235}}{180} tenglamasini yeching, bunda ± musbat. 1710 ni 6\sqrt{235} ga qo'shish.

$$x=\frac{6\sqrt{235}+1710}{180}$$

1710+6\sqrt{235} ni 180 ga bo'lish.

$$x=\frac{\sqrt{235}}{30}+\frac{19}{2}$$

x=\frac{1710±6\sqrt{235}}{180} tenglamasini yeching, bunda ± manfiy. 1710 dan 6\sqrt{235} ni ayirish.

$$x=\frac{1710-6\sqrt{235}}{180}$$

1710-6\sqrt{235} ni 180 ga bo'lish.

$$x=-\frac{\sqrt{235}}{30}+\frac{19}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{235}}{30}+\frac{19}{2} x=-\frac{\sqrt{235}}{30}+\frac{19}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

90 ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(90x-900\right)\left(x-9\right)=1$$

90x-900 ga x-9 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$90x^{2}-1710x+8100=1$$

Ikkala tarafdan 8100 ni ayirish.

$$90x^{2}-1710x=1-8100$$

-8099 olish uchun 1 dan 8100 ni ayirish.

$$90x^{2}-1710x=-8099$$

Ikki tarafini 90 ga bo‘ling.

$$\frac{90x^{2}-1710x}{90}=-\frac{8099}{90}$$

90 ga bo'lish 90 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{1710}{90}\right)x=-\frac{8099}{90}$$

-1710 ni 90 ga bo'lish.

$$x^{2}-19x=-\frac{8099}{90}$$

-19 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{19}{2} olish uchun. Keyin, -\frac{19}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-19x+\left(-\frac{19}{2}\right)^{2}=-\frac{8099}{90}+\left(-\frac{19}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{19}{2} kvadratini chiqarish.

$$x^{2}-19x+\frac{361}{4}=-\frac{8099}{90}+\frac{361}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{8099}{90} ni \frac{361}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-19x+\frac{361}{4}=\frac{47}{180}$$

x^{2}-19x+\frac{361}{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.

$$\left(x-\frac{19}{2}\right)^{2}=\frac{47}{180}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{19}{2}\right)^{2}}=\sqrt{\frac{47}{180}}$$

Qisqartirish.

$$x-\frac{19}{2}=\frac{\sqrt{235}}{30} x-\frac{19}{2}=-\frac{\sqrt{235}}{30}$$

\frac{19}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{235}}{30}+\frac{19}{2} x=-\frac{\sqrt{235}}{30}+\frac{19}{2}$$