Question

The sum of squares of two consecutive natural numbers is 244; find the numbers.

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Answer 1

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Answer 2

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The sum of squares of two “consecutive natural number” is 244, the numbers will be “12 and 10”.    

Given:  

Sum of squares of two consecutive natural number is 244.

Solution:  

Let us consider the first number as x, then the second number will be x + 2  

It is given that the sum of squares of two consecutive natural number is 244.

This can be written in equation as under:

⇒(x)²+(x+2)²=244

⇒x²+x²+4x+4=244

⇒2x²+4x=244−4

⇒2x²+4x=240

⇒2x²+4x−240=0

⇒2(x²+2x−120)=0

⇒(x²+2x−120)=0

⇒x(x+12)−10(x+12)=0

⇒(x−10)(x+12)=0

⇒x=10,−12

Thus, non be x= 12 & x = 10.

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