20^2+left(15tright)^2-left(12+15tright)^2/60t=frac{34^2+{left(15tright)}^2-{left(30+15tright)}^2}{-102t} eching

$$\frac{ { 20 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(12+15t \right) }^{ 2 } }{ 60t } = \frac{ { 34 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(30+15t \right) }^{ 2 } }{ -102t }$$

t uchun yechish

$$t=\frac{16}{35}\approx 0,457142857$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

t qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 1020t ga, 60t,-102t ning eng kichik karralisiga ko‘paytiring.

$$17\left(20^{2}+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$17\left(400+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

\left(15t\right)^{2} ni kengaytirish.

$$17\left(400+15^{2}t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$17\left(400+225t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(12+15t\right)^{2} kengaytirilishi uchun ishlating.

$$17\left(400+225t^{2}-\left(144+360t+225t^{2}\right)\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

144+360t+225t^{2} teskarisini topish uchun har birining teskarisini toping.

$$17\left(400+225t^{2}-144-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

256 olish uchun 400 dan 144 ni ayirish.

$$17\left(256+225t^{2}-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

0 ni olish uchun 225t^{2} va -225t^{2} ni birlashtirish.

$$17\left(256-360t\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

17 ga 256-360t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4352-6120t=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

2 daraja ko‘rsatkichini 34 ga hisoblang va 1156 ni qiymatni oling.

$$4352-6120t=-10\left(1156+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

\left(15t\right)^{2} ni kengaytirish.

$$4352-6120t=-10\left(1156+15^{2}t^{2}-\left(30+15t\right)^{2}\right)$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$4352-6120t=-10\left(1156+225t^{2}-\left(30+15t\right)^{2}\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(30+15t\right)^{2} kengaytirilishi uchun ishlating.

$$4352-6120t=-10\left(1156+225t^{2}-\left(900+900t+225t^{2}\right)\right)$$

900+900t+225t^{2} teskarisini topish uchun har birining teskarisini toping.

$$4352-6120t=-10\left(1156+225t^{2}-900-900t-225t^{2}\right)$$

256 olish uchun 1156 dan 900 ni ayirish.

$$4352-6120t=-10\left(256+225t^{2}-900t-225t^{2}\right)$$

0 ni olish uchun 225t^{2} va -225t^{2} ni birlashtirish.

$$4352-6120t=-10\left(256-900t\right)$$

-10 ga 256-900t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4352-6120t=-2560+9000t$$

Ikkala tarafdan 9000t ni ayirish.

$$4352-6120t-9000t=-2560$$

-15120t ni olish uchun -6120t va -9000t ni birlashtirish.

$$4352-15120t=-2560$$

Ikkala tarafdan 4352 ni ayirish.

$$-15120t=-2560-4352$$

-6912 olish uchun -2560 dan 4352 ni ayirish.

$$-15120t=-6912$$

Ikki tarafini -15120 ga bo‘ling.

$$t=\frac{-6912}{-15120}$$

\frac{-6912}{-15120} ulushini -432 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t=\frac{16}{35}$$