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प्रश्न
The sum of a number and its reciprocal is 4.25; the number is ______.
पर्याय
`2 or 1/2`
`4 or 1/4`
`1/5 or 5`
`1/3 or 3`
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उत्तर
The sum of a number and its reciprocal is 4.25; the number is `underlinebb(4 or 1/4)`.
Explanation:
Let the number be x
Then `x + 1/x = 4.25 = 425/100 = 17/4`
`\implies (x^2 + 1)/x = 17/4`
`\implies` 4(x2 + 1) = 17x
`\implies` 4x2 + 4 – 17x = 0
`\implies` 4x2 – 16x – x + 4 = 0
`\implies` 4x(x – 4) – 1(x – 4) = 0
`\implies` (x – 4)(4x – 1) = 0
Either x – 4 = 0 or 4x – 1 = 0
`\implies x = 4` or `x = 1/4`
`\implies x = 4` or `1/4`
संबंधित प्रश्न
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 a number and its reciprocal is 4.25. Find the number.
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.
Three positive numbers are in the ratio `1/2 : 1/3 : 1/4`. Find the numbers if the sum of their squares is 244.
Divide 20 into two parts such that three times the square of one part exceeds the other part by 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.
Given that the sum of the squares of the first seven natural numbers is 140, then their mean is ______.
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 ______.
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 ______.
