8-t=sqrt{5t^2+64-16t} eching

$$8 - t = \sqrt { 5 t ^ { 2 } + 64 - 16 t }$$

t uchun yechish

$$t=0$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(8-t\right)^{2}=\left(\sqrt{5t^{2}+64-16t}\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(8-t\right)^{2} kengaytirilishi uchun ishlating.

$$64-16t+t^{2}=\left(\sqrt{5t^{2}+64-16t}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{5t^{2}+64-16t} ga hisoblang va 5t^{2}+64-16t ni qiymatni oling.

$$64-16t+t^{2}=5t^{2}+64-16t$$

Ikkala tarafdan 5t^{2} ni ayirish.

$$64-16t+t^{2}-5t^{2}=64-16t$$

-4t^{2} ni olish uchun t^{2} va -5t^{2} ni birlashtirish.

$$64-16t-4t^{2}=64-16t$$

16t ni ikki tarafga qo’shing.

$$64-16t-4t^{2}+16t=64$$

0 ni olish uchun -16t va 16t ni birlashtirish.

$$64-4t^{2}=64$$

Ikkala tarafdan 64 ni ayirish.

$$-4t^{2}=64-64$$

0 olish uchun 64 dan 64 ni ayirish.

$$-4t^{2}=0$$

Ikki tarafini -4 ga bo‘ling. Nol bo‘lmagan har qanday sonni nolga ko‘paytirsangiz, nol bo‘ladi.

$$t^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$t=0 t=0$$

Tenglama yechildi. Yechimlar bir xil.

$$t=0$$

8-t=\sqrt{5t^{2}+64-16t} tenglamasida t uchun 0 ni almashtiring.

$$8-0=\sqrt{5\times 0^{2}+64-16\times 0}$$

Qisqartirish. t=0 tenglamani qoniqtiradi.

$$8=8$$

8-t=\sqrt{5t^{2}-16t+64} tenglamasi noyob yechimga ega.

$$t=0$$