Question:
If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?
If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?
Updated On: Nov 17, 2025
- \(\sqrt{(\frac{3}{2})}\)
- \(\sqrt{(\frac{5}{2})}\)
- \(\sqrt{(\frac{5}{4})}\)
- \(\sqrt{(\frac{3}{4})}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A):\(\sqrt{(\frac{3}{2})}\).
\(\frac{5(4x^2+1)-3x}{4x}=8\)
20x2+ 5 - 3x = 32x
20x2+ 5 = 35x
4x2- 7x + 1 = 0
4x2+ 1 = 7x... (i)
\(Now, (\sqrt2x-\frac{1}{\sqrt2x})=2x-2+\frac{1}{2x}\)
=\(\frac{ (4x2- 4x + 1)}{2x}\)
= \(\frac{(7x - 4x)}{2x}\) (from (i))
Therefore, \((\sqrt2x-\frac{1}{\sqrt2x})=\sqrt\frac{3}{2}\)
\(\frac{5(4x^2+1)-3x}{4x}=8\)
20x2+ 5 - 3x = 32x
20x2+ 5 = 35x
4x2- 7x + 1 = 0
4x2+ 1 = 7x... (i)
\(Now, (\sqrt2x-\frac{1}{\sqrt2x})=2x-2+\frac{1}{2x}\)
=\(\frac{ (4x2- 4x + 1)}{2x}\)
= \(\frac{(7x - 4x)}{2x}\) (from (i))
Therefore, \((\sqrt2x-\frac{1}{\sqrt2x})=\sqrt\frac{3}{2}\)
Was this answer helpful?
0
0
Top Questions on Number Systems
- Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?
- For the number \(N = 2^3 \times 3^7 \times 5^7 \times 7^9 \times 10!\), how many factors are perfect squares and also multiples of 420?
- CAT - 2025
- Quantitative Aptitude
- Number Systems
- In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?
- CAT - 2025
- Quantitative Aptitude
- Number Systems
- If the HCF of two numbers is 15 and their product is 1800, find the LCM.
- If a man covers one-third distance at speeds 10 km/h, 20 km/h, and 60 km/h, find the average speed.
View More Questions
Questions Asked in CAT exam
- Let $f(x) = \dfrac{x}{2x-1}$ and $g(x) = \dfrac{x}{x-1}$. Then, the domain of the function \[ h(x) = f(g(x)) + g(f(x)) \] is all real numbers except:
- CAT - 2025
- Number System
- The number of divisors of $(2^6 \times 3^5 \times 5^3 \times 7^2)$, which are of the form $(3r + 1)$, where $r$ is a non-negative integer, is:
- CAT - 2025
- Number System
- The sum of digits of the number $(625)^{65} \times (128)^{36}$ is:
- CAT - 2025
- Number System
- Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is:
- CAT - 2025
- Time and Work
- If $m$ and $n$ are integers such that $(m+2n)(2m+n)=27$, then the maximum possible value of $2m-3n$ is:
- CAT - 2025
- Number System
View More Questions