Question

the difference between two numbers is 6 and the difference between their squares is 72. Find the numbers.​

Answer 1

Answer:

The numbers are 9 and 3

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Answer 2

Given :

The Difference between two numbers is 6 and The difference between their Squares is 72.

To Find :

Find the numbers.

Solution :

Let the numbers be x and y.

According to the Question, The Equations are

x - y = 6 ___ ①

x² - y² = 72 ___ ②

from eq①,

x = 6 + y

substitute x = 6 + y in eq②, we get

⇒ (6 + y)² - y² = 72

⇒ 36 + y² + 12y - y² = 72

⇒ 12y + 36 = 72

⇒ 12y = 36

⇒ y = 3

then, Substituting y's value.

⇒ x = 6 + 3

⇒ x = 9

FINAL ANSWER :

The Numbers are 9 and 3.