Advertisements
Advertisements
Question
The sum of the squares of two consecutive natural numbers is 41. Find the numbers.
Advertisements
Solution
Let the numbers be x and x + 1.
From the given information,
x2 + (x + 1)2 = 41
2x2 + 2x + 1 – 41 = 0
x2 + x – 20 = 0
(x + 5)(x – 4) = 0
x = –5, 4
But, –5 is not a natural number.
So, x = 4.
Thus, the numbers are 4 and 5.
APPEARS IN
RELATED QUESTIONS
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.
Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.
The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.
Given that the sum of the squares of the first seven natural numbers is 140, then their mean is ______.
The sum of two natural numbers is 5 and the sum of their reciprocals is `5/6`, the numbers are ______.
The product of two consecutive even whole numbers is 24, the numbers are ______.
The sum of the squares of two consecutive integers is 41. The integers are ______.
The difference between the digits of a two-digit number is 2 and the product of digits is 24. If tens digit is bigger, the number is ______.
If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is ______.
The sum of two whole numbers is 18 and their product is 45, the numbers are ______.
