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

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

t uchun yechish

$$t=-400$$

$$t=120$$

Kvadrat tenglamalaridan foydalanish qoidalari

t qiymati -480,0 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.

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

280t ni olish uchun 480t va -200t ni birlashtirish.

$$t^{2}+280t=48000$$

Ikkala tarafdan 48000 ni ayirish.

$$t^{2}+280t-48000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 280 ni b va -48000 ni c bilan almashtiring.

$$t=\frac{-280±\sqrt{280^{2}-4\left(-48000\right)}}{2}$$

280 kvadratini chiqarish.

$$t=\frac{-280±\sqrt{78400-4\left(-48000\right)}}{2}$$

-4 ni -48000 marotabaga ko'paytirish.

$$t=\frac{-280±\sqrt{78400+192000}}{2}$$

78400 ni 192000 ga qo'shish.

$$t=\frac{-280±\sqrt{270400}}{2}$$

270400 ning kvadrat ildizini chiqarish.

$$t=\frac{-280±520}{2}$$

t=\frac{-280±520}{2} tenglamasini yeching, bunda ± musbat. -280 ni 520 ga qo'shish.

$$t=\frac{240}{2}$$

240 ni 2 ga bo'lish.

$$t=120$$

t=\frac{-280±520}{2} tenglamasini yeching, bunda ± manfiy. -280 dan 520 ni ayirish.

$$t=-\frac{800}{2}$$

-800 ni 2 ga bo'lish.

$$t=-400$$

Tenglama yechildi.

$$t=120 t=-400$$

Kvadratni yakunlash bo'yicha qadamlar

t qiymati -480,0 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.

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

280t ni olish uchun 480t va -200t ni birlashtirish.

$$t^{2}+280t=48000$$

280 ni bo‘lish, x shartining koeffitsienti, 2 ga 140 olish uchun. Keyin, 140 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}+280t+140^{2}=48000+140^{2}$$

140 kvadratini chiqarish.

$$t^{2}+280t+19600=48000+19600$$

48000 ni 19600 ga qo'shish.

$$t^{2}+280t+19600=67600$$

t^{2}+280t+19600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t+140\right)^{2}=67600$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t+140\right)^{2}}=\sqrt{67600}$$

Qisqartirish.

$$t+140=260 t+140=-260$$

Tenglamaning ikkala tarafidan 140 ni ayirish.

$$t=120 t=-400$$