ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If a = 2 then the value of a³ + 27a² + 243a + 631 is -

Solution:
Given,
a = 2

Now, 
 a³ + 27a² + 243a + 631
= a³ + 3 . a² . 9 + 3 . a . 9² + 9³ - 98
= (a + 9)³ - 98
= (2 + 9)³ - 98
= 1331 - 98
= 1233

Question: If x + 1/x = 99, find the value of 100x/(2x² + 2 + 102x) is?

Solution:
x + 1/x = 99
(x² + 1)/x = 99
x² + 1 = 99x
2(x² + 1) = 99x × 2
2x² + 2 = 198x

100x/(2x² + 2 + 102x) = 100x/(198x + 102x)
= 100x/300x
= 1/3

Question:

Solution:
Given,
(2p + 1/p) = 4
⇒ (1/2) (2p + 1/p) = 4 × 1/2
⇒ p + 1/2p = 2

Now, (p³ + 1/8p³) = (p)³ + (1/2p)³
= (p + 1/2p)³ - 3 . p . 1/2p . (p + 1/2p)
= (2)³ - 3 . (1/2) . 2
= 8 - 3
= 5

Question: If , then the value of

Solution:
Given, x + 1/x =1
⇒ (x² + 1)/x = 1
 ⇒ x² - x = - 1

Now, 
3/(x² - x + 7)
= 3/( - 1 + 7) [x² - x = - 1]
= 3/6
= 1/2

Question:

Solution:
Given that,
x - 1/x = - √5
⇒ (x - 1/x)² = (- √5)²
⇒ x² + 1/x² - 2 . x . (1/x) = 5
⇒ x² + 1/x² = 5 + 2
⇒ (x² + 1/x²)² = 7
⇒ (x²)² + (1/x²)² + 2 . x² . (1/x²) = 49
⇒ x⁴ + 1/x⁴ = 49 - 2
∴ x⁴ + 1/x⁴ = 47

Question:

Solution:

Question: = ?

Solution:
(1/2) {(a + b)² + (a - b)²} 
= (1/2) (a² + 2ab + b² + a² - 2ab + b²)
= (1/2) {2 (a² + b²)}
= a² + b²