10beta*33/(beta*33-045)^2=9*33*2/(33-045)^2 eching

$$\frac { 10 \beta \times 33 } { ( \beta \times 33 - 045 ) ^ { 2 } } = \frac { 9 \times 33 \times 2 } { ( 33 - 045 ) ^ { 2 } }$$

β uchun yechish

$$\beta =\frac{5}{9}\approx 0,555555556$$

Faktorlash qadamlari

\beta qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 1089\beta ^{2} ga ko'paytirish.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

330 hosil qilish uchun 10 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

297 hosil qilish uchun 9 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 297\times 2$$

594 hosil qilish uchun 297 va 2 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 594$$

Ikkala tarafdan \beta ^{2}\times 594 ni ayirish.

$$330\beta -\beta ^{2}\times 594=0$$

-594 hosil qilish uchun -1 va 594 ni ko'paytirish.

$$330\beta -594\beta ^{2}=0$$

\beta omili.

$$\beta \left(330-594\beta \right)=0$$

Tenglamani yechish uchun \beta =0 va 330-594\beta =0 ni yeching.

$$\beta =0 \beta =\frac{5}{9}$$

\beta qiymati 0 teng bo‘lmaydi.

$$\beta =\frac{5}{9}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\beta qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 1089\beta ^{2} ga ko'paytirish.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

330 hosil qilish uchun 10 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

297 hosil qilish uchun 9 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 297\times 2$$

594 hosil qilish uchun 297 va 2 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 594$$

Ikkala tarafdan \beta ^{2}\times 594 ni ayirish.

$$330\beta -\beta ^{2}\times 594=0$$

-594 hosil qilish uchun -1 va 594 ni ko'paytirish.

$$330\beta -594\beta ^{2}=0$$

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.

$$-594\beta ^{2}+330\beta =0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -594 ni a, 330 ni b va 0 ni c bilan almashtiring.

$$\beta =\frac{-330±\sqrt{330^{2}}}{2\left(-594\right)}$$

330^{2} ning kvadrat ildizini chiqarish.

$$\beta =\frac{-330±330}{2\left(-594\right)}$$

2 ni -594 marotabaga ko'paytirish.

$$\beta =\frac{-330±330}{-1188}$$

\beta =\frac{-330±330}{-1188} tenglamasini yeching, bunda ± musbat. -330 ni 330 ga qo'shish.

$$\beta =\frac{0}{-1188}$$

0 ni -1188 ga bo'lish.

$$\beta =0$$

\beta =\frac{-330±330}{-1188} tenglamasini yeching, bunda ± manfiy. -330 dan 330 ni ayirish.

$$\beta =-\frac{660}{-1188}$$

\frac{-660}{-1188} ulushini 132 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\beta =\frac{5}{9}$$

Tenglama yechildi.

$$\beta =0 \beta =\frac{5}{9}$$

\beta qiymati 0 teng bo‘lmaydi.

$$\beta =\frac{5}{9}$$

Kvadratni yakunlash bo'yicha qadamlar

\beta qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 1089\beta ^{2} ga ko'paytirish.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

330 hosil qilish uchun 10 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

297 hosil qilish uchun 9 va 33 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 297\times 2$$

594 hosil qilish uchun 297 va 2 ni ko'paytirish.

$$330\beta =\beta ^{2}\times 594$$

Ikkala tarafdan \beta ^{2}\times 594 ni ayirish.

$$330\beta -\beta ^{2}\times 594=0$$

-594 hosil qilish uchun -1 va 594 ni ko'paytirish.

$$330\beta -594\beta ^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-594\beta ^{2}+330\beta =0$$

Ikki tarafini -594 ga bo‘ling.

$$\frac{-594\beta ^{2}+330\beta }{-594}=\frac{0}{-594}$$

-594 ga bo'lish -594 ga ko'paytirishni bekor qiladi.

$$\beta ^{2}+\frac{330}{-594}\beta =\frac{0}{-594}$$

\frac{330}{-594} ulushini 66 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\beta ^{2}-\frac{5}{9}\beta =\frac{0}{-594}$$

0 ni -594 ga bo'lish.

$$\beta ^{2}-\frac{5}{9}\beta =0$$

-\frac{5}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{18} olish uchun. Keyin, -\frac{5}{18} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$\beta ^{2}-\frac{5}{9}\beta +\left(-\frac{5}{18}\right)^{2}=\left(-\frac{5}{18}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{18} kvadratini chiqarish.

$$\beta ^{2}-\frac{5}{9}\beta +\frac{25}{324}=\frac{25}{324}$$

\beta ^{2}-\frac{5}{9}\beta +\frac{25}{324} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(\beta -\frac{5}{18}\right)^{2}=\frac{25}{324}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(\beta -\frac{5}{18}\right)^{2}}=\sqrt{\frac{25}{324}}$$

Qisqartirish.

$$\beta -\frac{5}{18}=\frac{5}{18} \beta -\frac{5}{18}=-\frac{5}{18}$$

\frac{5}{18} ni tenglamaning ikkala tarafiga qo'shish.

$$\beta =\frac{5}{9} \beta =0$$

\beta qiymati 0 teng bo‘lmaydi.

$$\beta =\frac{5}{9}$$