প্রশ্ন: x - 1/x = 1 হলে, x3 - (1/x)3 এর মান কত?

সমাধান:

দেওয়া আছে,

x - 1/x = 1

এখন,

x3 - (1/x)3 = {x - (1/x)}3 + 3.x.(1/x) {x - (1/x)}

= 13 + 3 × 1

= 4

Question: If 5x + y = 25 and 5x - y = 5, then what are the values of x and y respectively?

Solution:

Given,

5x+y = 25

⇒ 5x + y = 52

⇒ x + y = 2 .......(1)

Again,

5x - y = 5

⇒ 5x - y = 51

⇒ x - y = 1 ........(2)

Now, solving (1) and (2) we get,

x + y + x - y = 2 + 1

⇒ 2x = 3

∴ x = 3/2

Now,

x + y = 2

⇒ 3/2 + y = 2

⇒ y = 2 - (3/2)

​⇒ y = 1/2

​

​(x, y) = (3/2, 1/2)

প্রশ্ন: a = 2b = 3c এবং abc = 288 হলে c এর মান কত?

সমাধান:
দেওয়া আছে,
a = 2b = 3c এবং abc = 288

∴ a = 3c 
এবং
2b = 3c 
⇒ b = 3c/2

এখন,
abc = 288
⇒ 3c × (3c/2) × c = 288
⇒ 9c3 = 288 × 2
⇒ c3 = (288 × 2)/9
⇒ c3 = 64
⇒ c3 = 43
⇒ c = 4