The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

Let the two numbers be x and y. So, x \- y = 3 .............(1) And, x 2 \- y 2 = 69 Using the formula [∵ (x 2 \- y 2 ) = (x \- y)(x \+ y)] ⇒ (x \- y)(x \+ y) = 69 Using eq (1), we get ⇒ 3(x \+ y) = 69 ⇒ x \+ y = ⇒ x \+ y = 23 .............(2) Adding (1) and (2) ⇒ (x \- y) \+ (x \+ y) = 3 \+ 23 ⇒ x \- y \+ x \+ y = 26 ⇒ 2x = 26 ⇒ x = ⇒ x = 13 Using eq (2) ⇒ y = 23 \- 13 ⇒ y = 10 Hence, the numbers are 13 and 10.

A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?

View Answer Bookmark Now

A man completed a trip of 136 km in 8 hours. Some parts of the trip was covered at 15 km/hr and the remaining at 18 km/hr. Find the part of the trip covered at 18 km/hr.

View Answer Bookmark Now

Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.

View Answer Bookmark Now

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.

View Answer Bookmark Now

Mathematics

The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

Linear Eqns One Variable

Related Questions

A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?

A man completed a trip of 136 km in 8 hours. Some parts of the trip was covered at 15 km/hr and the remaining at 18 km/hr. Find the part of the trip covered at 18 km/hr.

Two consecutive natural numbers are such that one-fourth of the smaller exceeds one-fifth of the greater by 1. Find the numbers.

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.