1.

The difference between two number is 3 and the difference between their cubes is 999. Find the difference between their squares.1. 632. 363. 814. 18

Answer» Correct Answer - Option 1 : 63

Given-

Difference between two number = 3

Difference between their cubes is 999

Formula Used-

x3 - y3 = (x - y)3 + 3xy(x - y)

(x + y)2 = (x - y)2 + 4xy

x2 - y2 = (x + y)(x - y)

Calculation-

Let the two numbers be x and y

According to Question-

x - y = 3 -------(i)

x3 - y3 = 999  -------------(ii)

⇒ (x - y)3 + 3xy(x - y) = 999

⇒ 27 + 9xy = 999

⇒ xy = 108

Now,

(x + y)2 = (x - y)2 + 4xy

⇒ (x + y)2 = 9 + 432

⇒ x + y = 21

x2 - y2 = (x + y)(x - y)

⇒ x2 - y2 = 21 × 3

⇒ 63

∴ Difference between their squares = 63


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