1200/a=1200/(a-20)+5 eching

$$\frac { 1200 } { a } = \frac { 1200 } { ( a - 20 ) } + 5$$

a uchun yechish

$$a=-10\sqrt{47}i+10\approx 10-68,556546004i$$

$$a=10+10\sqrt{47}i\approx 10+68,556546004i$$

Kvadrat tenglamalaridan foydalanish qoidalari

a qiymati 0,20 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a\left(a-20\right) ga, a,a-20 ning eng kichik karralisiga ko‘paytiring.

$$\left(a-20\right)\times 1200=a\times 1200+a\left(a-20\right)\times 5$$

a-20 ga 1200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+a\left(a-20\right)\times 5$$

a ga a-20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+\left(a^{2}-20a\right)\times 5$$

a^{2}-20a ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+5a^{2}-100a$$

1100a ni olish uchun a\times 1200 va -100a ni birlashtirish.

$$1200a-24000=1100a+5a^{2}$$

Ikkala tarafdan 1100a ni ayirish.

$$1200a-24000-1100a=5a^{2}$$

100a ni olish uchun 1200a va -1100a ni birlashtirish.

$$100a-24000=5a^{2}$$

Ikkala tarafdan 5a^{2} ni ayirish.

$$100a-24000-5a^{2}=0$$

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.

$$-5a^{2}+100a-24000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, 100 ni b va -24000 ni c bilan almashtiring.

$$a=\frac{-100±\sqrt{100^{2}-4\left(-5\right)\left(-24000\right)}}{2\left(-5\right)}$$

100 kvadratini chiqarish.

$$a=\frac{-100±\sqrt{10000-4\left(-5\right)\left(-24000\right)}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$a=\frac{-100±\sqrt{10000+20\left(-24000\right)}}{2\left(-5\right)}$$

20 ni -24000 marotabaga ko'paytirish.

$$a=\frac{-100±\sqrt{10000-480000}}{2\left(-5\right)}$$

10000 ni -480000 ga qo'shish.

$$a=\frac{-100±\sqrt{-470000}}{2\left(-5\right)}$$

-470000 ning kvadrat ildizini chiqarish.

$$a=\frac{-100±100\sqrt{47}i}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$a=\frac{-100±100\sqrt{47}i}{-10}$$

a=\frac{-100±100\sqrt{47}i}{-10} tenglamasini yeching, bunda ± musbat. -100 ni 100i\sqrt{47} ga qo'shish.

$$a=\frac{-100+100\sqrt{47}i}{-10}$$

-100+100i\sqrt{47} ni -10 ga bo'lish.

$$a=-10\sqrt{47}i+10$$

a=\frac{-100±100\sqrt{47}i}{-10} tenglamasini yeching, bunda ± manfiy. -100 dan 100i\sqrt{47} ni ayirish.

$$a=\frac{-100\sqrt{47}i-100}{-10}$$

-100-100i\sqrt{47} ni -10 ga bo'lish.

$$a=10+10\sqrt{47}i$$

Tenglama yechildi.

$$a=-10\sqrt{47}i+10 a=10+10\sqrt{47}i$$

Kvadratni yakunlash bo'yicha qadamlar

a qiymati 0,20 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a\left(a-20\right) ga, a,a-20 ning eng kichik karralisiga ko‘paytiring.

$$\left(a-20\right)\times 1200=a\times 1200+a\left(a-20\right)\times 5$$

a-20 ga 1200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+a\left(a-20\right)\times 5$$

a ga a-20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+\left(a^{2}-20a\right)\times 5$$

a^{2}-20a ga 5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1200a-24000=a\times 1200+5a^{2}-100a$$

1100a ni olish uchun a\times 1200 va -100a ni birlashtirish.

$$1200a-24000=1100a+5a^{2}$$

Ikkala tarafdan 1100a ni ayirish.

$$1200a-24000-1100a=5a^{2}$$

100a ni olish uchun 1200a va -1100a ni birlashtirish.

$$100a-24000=5a^{2}$$

Ikkala tarafdan 5a^{2} ni ayirish.

$$100a-24000-5a^{2}=0$$

24000 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$100a-5a^{2}=24000$$

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

$$-5a^{2}+100a=24000$$

Ikki tarafini -5 ga bo‘ling.

$$\frac{-5a^{2}+100a}{-5}=\frac{24000}{-5}$$

-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.

$$a^{2}+\frac{100}{-5}a=\frac{24000}{-5}$$

100 ni -5 ga bo'lish.

$$a^{2}-20a=\frac{24000}{-5}$$

24000 ni -5 ga bo'lish.

$$a^{2}-20a=-4800$$

-20 ni bo‘lish, x shartining koeffitsienti, 2 ga -10 olish uchun. Keyin, -10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-20a+\left(-10\right)^{2}=-4800+\left(-10\right)^{2}$$

-10 kvadratini chiqarish.

$$a^{2}-20a+100=-4800+100$$

-4800 ni 100 ga qo'shish.

$$a^{2}-20a+100=-4700$$

a^{2}-20a+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a-10\right)^{2}=-4700$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-10\right)^{2}}=\sqrt{-4700}$$

Qisqartirish.

$$a-10=10\sqrt{47}i a-10=-10\sqrt{47}i$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$a=10+10\sqrt{47}i a=-10\sqrt{47}i+10$$