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The difference between squares of two consecutive numbers is 31. Find the numbers.
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Answer 1

Answer :

Here, we are given that the difference between the squares of two consecutive numbers is 31 and we need to calculate the two numbers. For that, firstly we will assume the first number as any variable and for the second number we will add 1 to the variable, the resultant number will be the second number. And then by using the condition given in the question, we will get the value of the variables, consequently we will get the two numbers.

Solution :

Given :

• The difference between squares of two consecutive numbers = 31

To find :

• The two numbers

Solution :

Let,

• The first number = a
• The second number = a + 1

According to the question,

⇒ (First number)² - (Second number)² = 31

⇒ (a)² - (a + 1)² = 31

Using identity :

• (a + b)² = a² + b² + 2ab

⇒ a² - (a² + 1 + 2(a)(1)) = 31

⇒ a² - (a² + 1 + 2a) = 31

⇒ a² - a² - 1 - 2a = 31

⇒ - 1 - 2a = 31

⇒ - 2a = 31 + 1

⇒ - 2a = 32

⇒ - a = 32/2

⇒ - a = 16

⇒ a = - 16

• The value of a = - 16

Substituting the value of 'a' :

FIRST NUMBER :

⇒ First number = a

⇒ First number = - 16

SECOND NUMBER :

⇒ Second number = a + 1

⇒ Second number = - 16 + 1

⇒ Second number = - 15

Therefore,

• The two numbers are - 16 and - 15