Advertisements
Advertisements
Question
Find two consecutive positive odd numbers, the sum of whose squares is 74.
Advertisements
Solution
Let the consecutive positive odd numbers be x and x + 2.
From the given information,
x2 + (x + 2)2 = 74
2x2 + 4x + 4 = 74
2x2 + 4x – 70 = 0
x2 + 2x – 35 = 0
(x + 7)(x – 5) = 0
x = –7, 5
Since, the numbers are positive, so, x = 5.
Thus, the numbers are 5 and 7.
RELATED QUESTIONS
The product of two consecutive integers is 56. Find the integers.
Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.
Given that the sum of the squares of the first seven natural numbers is 140, then their mean is ______.
The sum of a number and its reciprocal is 5.2. The number is ______.
The sum of the squares of two consecutive integers is 41. The integers are ______.
The product of two whole numbers, each greater than 4, is 35; the numbers 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 ______.
The sum of a number and its reciprocal is 4.25; the number is ______.
The sum of two whole numbers is 18 and their product is 45, the numbers are ______.
