05*10^-3=1/2*350*383*10^-7*25*(3-y-07)^2 eching

$$05 \times 10 ^ { - 3 } = \frac { 1 } { 2 } \times 350 \times 383 \times 10 ^ { - 7 } \times 25 \times ( 3 - y - 07 ) ^ { 2 }$$

y uchun yechish

$$y=3$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$0\times 10^{-3}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$0\times \frac{1}{1000}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va \frac{1}{1000} ni ko'paytirish.

$$0=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

175 hosil qilish uchun \frac{1}{2} va 350 ni ko'paytirish.

$$0=175\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

67025 hosil qilish uchun 175 va 383 ni ko'paytirish.

$$0=67025\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-7 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000000} ni qiymatni oling.

$$0=67025\times \frac{1}{10000000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{400000} hosil qilish uchun 67025 va \frac{1}{10000000} ni ko'paytirish.

$$0=\frac{2681}{400000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{16000} hosil qilish uchun \frac{2681}{400000} va 25 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va 7 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\right)^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{2681}{16000}\left(3-y-0\right)^{2}=0$$

Ikki tarafini \frac{16000}{2681} va teskari kasri \frac{2681}{16000} ga ko‘paytiring. Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\left(3-y-0\right)^{2}=0$$

Shartlarni qayta saralash.

$$\left(-y+3\right)^{2}=0$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-y+3\right)^{2} kengaytirilishi uchun ishlating.

$$y^{2}-6y+9=0$$

Bu tenglamani yechish uchun y^{2}+\left(a+b\right)y+ab=\left(y+a\right)\left(y+b\right) formulasi yordamida y^{2}-6y+9 ni faktorlang. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-6 ab=9$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 9-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-9 -3,-3$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-9=-10 -3-3=-6$$

Yechim – -6 yigʻindisini beruvchi juftlik.

$$a=-3 b=-3$$

Faktorlangan \left(y+a\right)\left(y+b\right) ifodani olingan qiymatlar bilan qaytadan yozing.

$$\left(y-3\right)\left(y-3\right)$$

Binom kvadrat sifatid qayta yozish.

$$\left(y-3\right)^{2}$$

Tenglamani yechish uchun y-3=0 ni yeching.

$$y=3$$

Guruhlash orqali faktorlash qadamlari

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$0\times 10^{-3}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$0\times \frac{1}{1000}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va \frac{1}{1000} ni ko'paytirish.

$$0=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

175 hosil qilish uchun \frac{1}{2} va 350 ni ko'paytirish.

$$0=175\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

67025 hosil qilish uchun 175 va 383 ni ko'paytirish.

$$0=67025\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-7 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000000} ni qiymatni oling.

$$0=67025\times \frac{1}{10000000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{400000} hosil qilish uchun 67025 va \frac{1}{10000000} ni ko'paytirish.

$$0=\frac{2681}{400000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{16000} hosil qilish uchun \frac{2681}{400000} va 25 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va 7 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\right)^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{2681}{16000}\left(3-y-0\right)^{2}=0$$

Ikki tarafini \frac{16000}{2681} va teskari kasri \frac{2681}{16000} ga ko‘paytiring. Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\left(3-y-0\right)^{2}=0$$

Shartlarni qayta saralash.

$$\left(-y+3\right)^{2}=0$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-y+3\right)^{2} kengaytirilishi uchun ishlating.

$$y^{2}-6y+9=0$$

Tenglamani yechish uchun guruhlash orqali chap qoʻl tomonni faktorlang. Avvalo, chap qoʻl tomon y^{2}+ay+by+9 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-6 ab=1\times 9=9$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 9-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-9 -3,-3$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-9=-10 -3-3=-6$$

Yechim – -6 yigʻindisini beruvchi juftlik.

$$a=-3 b=-3$$

y^{2}-6y+9 ni \left(y^{2}-3y\right)+\left(-3y+9\right) sifatida qaytadan yozish.

$$\left(y^{2}-3y\right)+\left(-3y+9\right)$$

Birinchi guruhda y ni va ikkinchi guruhda -3 ni faktordan chiqaring.

$$y\left(y-3\right)-3\left(y-3\right)$$

Distributiv funktsiyasidan foydalangan holda y-3 umumiy terminini chiqaring.

$$\left(y-3\right)\left(y-3\right)$$

Binom kvadrat sifatid qayta yozish.

$$\left(y-3\right)^{2}$$

Tenglamani yechish uchun y-3=0 ni yeching.

$$y=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$0\times 10^{-3}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$0\times \frac{1}{1000}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va \frac{1}{1000} ni ko'paytirish.

$$0=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

175 hosil qilish uchun \frac{1}{2} va 350 ni ko'paytirish.

$$0=175\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

67025 hosil qilish uchun 175 va 383 ni ko'paytirish.

$$0=67025\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-7 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000000} ni qiymatni oling.

$$0=67025\times \frac{1}{10000000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{400000} hosil qilish uchun 67025 va \frac{1}{10000000} ni ko'paytirish.

$$0=\frac{2681}{400000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{16000} hosil qilish uchun \frac{2681}{400000} va 25 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va 7 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\right)^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{2681}{16000}\left(3-y-0\right)^{2}=0$$

Ikki tarafini \frac{16000}{2681} va teskari kasri \frac{2681}{16000} ga ko‘paytiring. Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\left(3-y-0\right)^{2}=0$$

Shartlarni qayta saralash.

$$\left(-y+3\right)^{2}=0$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-y+3\right)^{2} kengaytirilishi uchun ishlating.

$$y^{2}-6y+9=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va 9 ni c bilan almashtiring.

$$y=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 9}}{2}$$

-6 kvadratini chiqarish.

$$y=\frac{-\left(-6\right)±\sqrt{36-4\times 9}}{2}$$

-4 ni 9 marotabaga ko'paytirish.

$$y=\frac{-\left(-6\right)±\sqrt{36-36}}{2}$$

36 ni -36 ga qo'shish.

$$y=\frac{-\left(-6\right)±\sqrt{0}}{2}$$

0 ning kvadrat ildizini chiqarish.

$$y=-\frac{-6}{2}$$

-6 ning teskarisi 6 ga teng.

$$y=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$y=3$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$0\times 10^{-3}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$0\times \frac{1}{1000}=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va \frac{1}{1000} ni ko'paytirish.

$$0=\frac{1}{2}\times 350\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

175 hosil qilish uchun \frac{1}{2} va 350 ni ko'paytirish.

$$0=175\times 383\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

67025 hosil qilish uchun 175 va 383 ni ko'paytirish.

$$0=67025\times 10^{-7}\times 25\left(3-y-0\times 7\right)^{2}$$

-7 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000000} ni qiymatni oling.

$$0=67025\times \frac{1}{10000000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{400000} hosil qilish uchun 67025 va \frac{1}{10000000} ni ko'paytirish.

$$0=\frac{2681}{400000}\times 25\left(3-y-0\times 7\right)^{2}$$

\frac{2681}{16000} hosil qilish uchun \frac{2681}{400000} va 25 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\times 7\right)^{2}$$

0 hosil qilish uchun 0 va 7 ni ko'paytirish.

$$0=\frac{2681}{16000}\left(3-y-0\right)^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{2681}{16000}\left(3-y-0\right)^{2}=0$$

Ikki tarafini \frac{16000}{2681} va teskari kasri \frac{2681}{16000} ga ko‘paytiring. Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\left(3-y-0\right)^{2}=0$$

Shartlarni qayta saralash.

$$\left(-y+3\right)^{2}=0$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(-y+3\right)^{2} kengaytirilishi uchun ishlating.

$$y^{2}-6y+9=0$$

y^{2}-6y+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-3\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-3\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$y-3=0 y-3=0$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$y=3 y=3$$

Tenglama yechildi. Yechimlar bir xil.

$$y=3$$