Question:
If u2+(u-2v-1)2 = -4v(u+v),then what is the value of u+3v?
If u2+(u-2v-1)2 = -4v(u+v),then what is the value of u+3v?
Updated On: Sep 30, 2024
- 1/4
- 0
- 1/2
- -1/4
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is (D):
u2+(u-2v-1)2=-4v(u+v)
⇒ u2+u2+4v2+1-4uv+4v-2u+4vu+4v2 = 0
⇒ 2u2-2u+8v2+4v+1 = 0
⇒ 2(u2-u+1/4)+2(4v2+2v+1/4) = 0
⇒ 2(u-1/2)2+2(2v+1/2)2 = 0
⇒ u-1/2 = 0;2v+1/2 = 0
u = 1/2 and v = -1/4
u+3v = 1/2 - 3/4 = -1/4
Was this answer helpful?
0
0
Top Questions on Number Systems
- Prove that $\sqrt{3}$ is an irrational number.
- CBSE Class X - 2024
- Mathematics
- Number Systems
- Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4- digit number is divisible by a? - Prove that $\sqrt{3}$ is an irrational number.
- CBSE Class X - 2024
- Mathematics
- Number Systems
- If abc > 0, such that a,b,c are integers then which of the following must be true?
- A king has distributed all his rare jewels in three boxes. The first box contains 1/3 of the rare jewels, while the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains 66 rare jewels.
How many rare jewels does the king have?
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Time and Work
- 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
- 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
- A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
- CAT - 2024
- Mixtures and Allegations
View More Questions