(85-30)(85+36)/(85-b)(85+b)=11/20 eching

$$\frac { ( 85 - 30 ) ( 85 + 36 ) } { ( 85 - b ) ( 85 + b ) } = \frac { 11 } { 20 }$$

b uchun yechish

$$b=-5\sqrt{195}i\approx -0-69,821200219i$$

$$b=5\sqrt{195}i\approx 69,821200219i$$

Kvadrat ildizini topish bo'yicha qadamlar

b qiymati -85,85 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 20\left(b-85\right)\left(b+85\right) ga, \left(85-b\right)\left(85+b\right),20 ning eng kichik karralisiga ko‘paytiring.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

55 olish uchun 85 dan 30 ni ayirish.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

-1100 hosil qilish uchun -20 va 55 ni ko'paytirish.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

121 olish uchun 85 va 36'ni qo'shing.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

-133100 hosil qilish uchun -1100 va 121 ni ko'paytirish.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

11 ga b-85 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

11b-935 ga b+85 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-133100=11b^{2}-79475$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$11b^{2}-79475=-133100$$

79475 ni ikki tarafga qo’shing.

$$11b^{2}=-133100+79475$$

-53625 olish uchun -133100 va 79475'ni qo'shing.

$$11b^{2}=-53625$$

Ikki tarafini 11 ga bo‘ling.

$$b^{2}=\frac{-53625}{11}$$

-4875 ni olish uchun -53625 ni 11 ga bo‘ling.

$$b^{2}=-4875$$

Tenglama yechildi.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

b qiymati -85,85 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 20\left(b-85\right)\left(b+85\right) ga, \left(85-b\right)\left(85+b\right),20 ning eng kichik karralisiga ko‘paytiring.

$$-20\left(85-30\right)\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

55 olish uchun 85 dan 30 ni ayirish.

$$-20\times 55\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

-1100 hosil qilish uchun -20 va 55 ni ko'paytirish.

$$-1100\left(85+36\right)=11\left(b-85\right)\left(b+85\right)$$

121 olish uchun 85 va 36'ni qo'shing.

$$-1100\times 121=11\left(b-85\right)\left(b+85\right)$$

-133100 hosil qilish uchun -1100 va 121 ni ko'paytirish.

$$-133100=11\left(b-85\right)\left(b+85\right)$$

11 ga b-85 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-133100=\left(11b-935\right)\left(b+85\right)$$

11b-935 ga b+85 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-133100=11b^{2}-79475$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$11b^{2}-79475=-133100$$

133100 ni ikki tarafga qo’shing.

$$11b^{2}-79475+133100=0$$

53625 olish uchun -79475 va 133100'ni qo'shing.

$$11b^{2}+53625=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 11 ni a, 0 ni b va 53625 ni c bilan almashtiring.

$$b=\frac{0±\sqrt{0^{2}-4\times 11\times 53625}}{2\times 11}$$

0 kvadratini chiqarish.

$$b=\frac{0±\sqrt{-4\times 11\times 53625}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{-44\times 53625}}{2\times 11}$$

-44 ni 53625 marotabaga ko'paytirish.

$$b=\frac{0±\sqrt{-2359500}}{2\times 11}$$

-2359500 ning kvadrat ildizini chiqarish.

$$b=\frac{0±110\sqrt{195}i}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$b=\frac{0±110\sqrt{195}i}{22}$$

b=\frac{0±110\sqrt{195}i}{22} tenglamasini yeching, bunda ± musbat.

$$b=5\sqrt{195}i$$

b=\frac{0±110\sqrt{195}i}{22} tenglamasini yeching, bunda ± manfiy.

$$b=-5\sqrt{195}i$$

Tenglama yechildi.

$$b=5\sqrt{195}i b=-5\sqrt{195}i$$