ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: (x + y)² = ?

Solution: 
(x + y)² = x² + y² + 2xy
(x + y)² = (x - y)² + 4xy

Question: If a + b = √3 and a = √2 + b, what is the value of 4ab?

Solution: 
given,
a + b = √3
a = √2 + b
a - b = √2

4ab = (a + b)² - (a - b)²
= 3 - 2
= 1

Question: What should be added to 9p² + 14p so that the sum is a perfect square?

Solution:
(3p)² + 2.3p.(7/3) + (7/3)²
= (3p + 7/3)²

so, (7/3)² or, 49/9 should be added to make it a perfect square.

Question: (x + y)² + (x - y)² = ?

Solution:
(x + y)² + (x - y)²
= x² + y² + 2xy + x² - 2xy + y²
= 2x² + 2y²
= 2(x² + y²)

Question:

Solution: 

Question: If a³ - b³ = 513 and a - b = 3, What is the value of ab?

Solution: 
given,
a³ - b³ = 513
a - b = 3

we know that,
a³ - b³ = (a - b)³ + 3ab(a - b)
or, (a - b)³ + 3ab(a - b) = 513
or, 3³ + 3ab(3) = 513
or, 9ab = 513 - 27
or, ab = 486/9
∴ ab = 54