81b^2-126b+48=0 eching

$$81 b ^ { 2 } - 126 b + 48 = 0$$

b uchun yechish

$$b=\frac{2}{3}\approx 0,666666667$$

$$b=\frac{8}{9}\approx 0,888888889$$

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.

$$81b^{2}-126b+48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 81 ni a, -126 ni b va 48 ni c bilan almashtiring.

$$b=\frac{-\left(-126\right)±\sqrt{\left(-126\right)^{2}-4\times 81\times 48}}{2\times 81}$$

-126 kvadratini chiqarish.

$$b=\frac{-\left(-126\right)±\sqrt{15876-4\times 81\times 48}}{2\times 81}$$

-4 ni 81 marotabaga ko'paytirish.

$$b=\frac{-\left(-126\right)±\sqrt{15876-324\times 48}}{2\times 81}$$

-324 ni 48 marotabaga ko'paytirish.

$$b=\frac{-\left(-126\right)±\sqrt{15876-15552}}{2\times 81}$$

15876 ni -15552 ga qo'shish.

$$b=\frac{-\left(-126\right)±\sqrt{324}}{2\times 81}$$

324 ning kvadrat ildizini chiqarish.

$$b=\frac{-\left(-126\right)±18}{2\times 81}$$

-126 ning teskarisi 126 ga teng.

$$b=\frac{126±18}{2\times 81}$$

2 ni 81 marotabaga ko'paytirish.

$$b=\frac{126±18}{162}$$

b=\frac{126±18}{162} tenglamasini yeching, bunda ± musbat. 126 ni 18 ga qo'shish.

$$b=\frac{144}{162}$$

\frac{144}{162} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=\frac{8}{9}$$

b=\frac{126±18}{162} tenglamasini yeching, bunda ± manfiy. 126 dan 18 ni ayirish.

$$b=\frac{108}{162}$$

\frac{108}{162} ulushini 54 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=\frac{2}{3}$$

Tenglama yechildi.

$$b=\frac{8}{9} b=\frac{2}{3}$$

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.

$$81b^{2}-126b+48=0$$

Tenglamaning ikkala tarafidan 48 ni ayirish.

$$81b^{2}-126b+48-48=-48$$

O‘zidan 48 ayirilsa 0 qoladi.

$$81b^{2}-126b=-48$$

Ikki tarafini 81 ga bo‘ling.

$$\frac{81b^{2}-126b}{81}=-\frac{48}{81}$$

81 ga bo'lish 81 ga ko'paytirishni bekor qiladi.

$$b^{2}+\left(-\frac{126}{81}\right)b=-\frac{48}{81}$$

\frac{-126}{81} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b^{2}-\frac{14}{9}b=-\frac{48}{81}$$

\frac{-48}{81} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b^{2}-\frac{14}{9}b=-\frac{16}{27}$$

-\frac{14}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{9} olish uchun. Keyin, -\frac{7}{9} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$b^{2}-\frac{14}{9}b+\left(-\frac{7}{9}\right)^{2}=-\frac{16}{27}+\left(-\frac{7}{9}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{9} kvadratini chiqarish.

$$b^{2}-\frac{14}{9}b+\frac{49}{81}=-\frac{16}{27}+\frac{49}{81}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{16}{27} ni \frac{49}{81} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$b^{2}-\frac{14}{9}b+\frac{49}{81}=\frac{1}{81}$$

b^{2}-\frac{14}{9}b+\frac{49}{81} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(b-\frac{7}{9}\right)^{2}=\frac{1}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b-\frac{7}{9}\right)^{2}}=\sqrt{\frac{1}{81}}$$

Qisqartirish.

$$b-\frac{7}{9}=\frac{1}{9} b-\frac{7}{9}=-\frac{1}{9}$$

\frac{7}{9} ni tenglamaning ikkala tarafiga qo'shish.

$$b=\frac{8}{9} b=\frac{2}{3}$$