1/100=1/t-480+1/t eching

$$\frac{ 1 }{ 100 } = \frac{ 1 }{ t-480 } + \frac{ 1 }{ t }$$

t uchun yechish

$$t=80$$

$$t=600$$

Kvadrat tenglamalaridan foydalanish qoidalari

t qiymati 0,480 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 100t\left(t-480\right) ga, 100,t-480,t ning eng kichik karralisiga ko‘paytiring.

$$t\left(t-480\right)=100t+100t-48000$$

t ga t-480 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$t^{2}-480t=100t+100t-48000$$

200t ni olish uchun 100t va 100t ni birlashtirish.

$$t^{2}-480t=200t-48000$$

Ikkala tarafdan 200t ni ayirish.

$$t^{2}-480t-200t=-48000$$

-680t ni olish uchun -480t va -200t ni birlashtirish.

$$t^{2}-680t=-48000$$

48000 ni ikki tarafga qo’shing.

$$t^{2}-680t+48000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -680 ni b va 48000 ni c bilan almashtiring.

$$t=\frac{-\left(-680\right)±\sqrt{\left(-680\right)^{2}-4\times 48000}}{2}$$

-680 kvadratini chiqarish.

$$t=\frac{-\left(-680\right)±\sqrt{462400-4\times 48000}}{2}$$

-4 ni 48000 marotabaga ko'paytirish.

$$t=\frac{-\left(-680\right)±\sqrt{462400-192000}}{2}$$

462400 ni -192000 ga qo'shish.

$$t=\frac{-\left(-680\right)±\sqrt{270400}}{2}$$

270400 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-680\right)±520}{2}$$

-680 ning teskarisi 680 ga teng.

$$t=\frac{680±520}{2}$$

t=\frac{680±520}{2} tenglamasini yeching, bunda ± musbat. 680 ni 520 ga qo'shish.

$$t=\frac{1200}{2}$$

1200 ni 2 ga bo'lish.

$$t=600$$

t=\frac{680±520}{2} tenglamasini yeching, bunda ± manfiy. 680 dan 520 ni ayirish.

$$t=\frac{160}{2}$$

160 ni 2 ga bo'lish.

$$t=80$$

Tenglama yechildi.

$$t=600 t=80$$

Kvadratni yakunlash bo'yicha qadamlar

t qiymati 0,480 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 100t\left(t-480\right) ga, 100,t-480,t ning eng kichik karralisiga ko‘paytiring.

$$t\left(t-480\right)=100t+100t-48000$$

t ga t-480 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$t^{2}-480t=100t+100t-48000$$

200t ni olish uchun 100t va 100t ni birlashtirish.

$$t^{2}-480t=200t-48000$$

Ikkala tarafdan 200t ni ayirish.

$$t^{2}-480t-200t=-48000$$

-680t ni olish uchun -480t va -200t ni birlashtirish.

$$t^{2}-680t=-48000$$

-680 ni bo‘lish, x shartining koeffitsienti, 2 ga -340 olish uchun. Keyin, -340 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-680t+\left(-340\right)^{2}=-48000+\left(-340\right)^{2}$$

-340 kvadratini chiqarish.

$$t^{2}-680t+115600=-48000+115600$$

-48000 ni 115600 ga qo'shish.

$$t^{2}-680t+115600=67600$$

t^{2}-680t+115600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-340\right)^{2}=67600$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-340\right)^{2}}=\sqrt{67600}$$

Qisqartirish.

$$t-340=260 t-340=-260$$

340 ni tenglamaning ikkala tarafiga qo'shish.

$$t=600 t=80$$