Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the numbers be p – 1, p and p + 1.
From the given information,
3(p + 1)2 = (p – 1)2 + p2 + 67
3p2 + 6p + 3 = p2 + 1 – 2p + p2 + 67
p2 + 8p – 65 = 0
(p + 13)(p – 5) = 0
p = –13, 5
Since, the numbers are positive so p cannot be equal to –13.
Thus, p = 5.
संबंधित प्रश्न
The sum of the squares of two consecutive natural numbers is 41. Find the numbers.
Find the two natural numbers which differ by 5 and the sum of whose squares is 97.
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
Find two consecutive positive odd numbers, the sum of whose squares is 74.
The product of two consecutive even whole numbers is 24, the numbers are ______.
The sum of a number and its reciprocal is 5.2. The number is ______.
Two integers differ by 2 and sum of their squares is 52. The integers are ______.
In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is ______.
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 ______.
