Advertisements
Advertisements
प्रश्न
The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.
Advertisements
उत्तर
Let the required fraction be `x/(2x + 1)`
From the given information,
`x/(2x + 1) + (2x + 1)/x = 2.9`
`(x^2 + 4x^2 + 1 + 4x)/(x(2x + 1)) = 29/10`
`(5x^2 + 1 + 4x)/(2x^2 + x) = 29/10`
`50x^2 + 10 + 40x = 58x^2 + 29x`
`8x^2 - 11x - 10 = 0`
`x = (11 +- sqrt(121 + 320))/16`
`x = (11+-sqrt441)/16`
`x = (11 +- 21)/16`
`x = 2, -5/8`
Thus, the required fraction is `2/5`
संबंधित प्रश्न
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 a number and its reciprocal is 4.25. Find the number.
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 S of first n even natural numbers is given by the relation S = n(n + 1). Find n, if the sum is 420.
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 ______.
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 sum of a number and its reciprocal is 4.25; the number is ______.
