4. the difference between the squares of two consecutive numbers is 31. find the numbers.

Text Solution

Solution : Let first number`=x`<br>The second number`=x+1`.<br>Given:<br>The difference between the squares of two consecutive numbers`=31`.<br>According to the question:<br>`(x+1)^2-x^2=31`<br>`x^2+2x+1-x^2=31`<br>`2x=31-1`<br>`2x=30`<br>`x=15`<br>`therefore` The first number`=15`<br>The second number`=15+1=16`<br>Hence, the numbers are `15, 16`.

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