Question:medium

\(\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}.\)
Find \( x \).

Updated On: Nov 24, 2025

Top Questions on Algebra

If \( a, b, c \) are all positive integers, with \( 4a>b \), then which of the following conditions is BOTH NECESSARY AND SUFFICIENT for the expression \[ \sqrt{(3)^a (21)^{3a-b} (49)^{2b+c}} \] to be a positive integer?
View Solution
For how many distinct real values of \( x \) does the equation below hold true? (Consider \( a>0 \)) \[ x^2 \log_a (16) - \log_a (64) \div \log_a (32) - x = 0 \]
View Solution
The market value of beams, made of a rare metal, has a unique property: the market value of any such beam is proportional to the square of its length. Due to an accident, one such beam got broken into two pieces having lengths in the ratio 4:9. Considering each broken piece as a separate beam, how much gain or loss, with respect to the market value of the original beam before the accident, is incurred?
View Solution
In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
\(R\) and \(S\) scored the same on the first test.
From the second test onwards, \(R\) consistently scored the same (a non-zero score).
The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
From the fifth test onwards, \(S\) scored the same as \(R\).
The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in CAT exam

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

CAT - 2024
Time and Work

View Solution

The number of all positive integers up to 500 with non-repeating digits is

CAT - 2024
Number Systems

View Solution

The midpoints of sides AB, BC, and AC in ∆ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ∆ABC is 1440 sq cm, then the area, in sq cm, of ∆XYZ is

CAT - 2024
Mensuration

View Solution

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

CAT - 2024
Profit and Loss

View Solution