Advertisements
Advertisements
Question
The sum of a number and its reciprocal is 4.25. Find the number.
Advertisements
Solution
Let the numbers be x and `1/x`
Form the given information,
`x + 1/x = 4.25`
`(x^2 + 1)/x = 425/100 = 17/4`
4x2 – 17x + 4 = 0
4x2 – 16x – x + 4 = 0
4x(x – 4) – 1(x – 4) = 0
(x – 4)(4x – 1) = 0
`x = 4,1/4`
`x = 4 => 1/x = 1/4`
`x = 1/4 => x = 4`
Thus, the number are 4 and `1/4`
APPEARS IN
RELATED QUESTIONS
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
The sum of the squares of two positive integers is 208. If the square of the large number is 18 times the smaller. Find the numbers.
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.
Find two consecutive positive odd numbers, the sum of whose squares is 74.
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.
The sum of two natural numbers is 5 and the sum of their reciprocals is `5/6`, the numbers are ______.
The sum of the squares of two consecutive integers is 41. 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 ______.
