Question:
If a2+b2=89 and a2-b2=39, then find the value of a3 - b3-3ab, (a, b >0).
If a2+b2=89 and a2-b2=39, then find the value of a3 - b3-3ab, (a, b >0).
Updated On: Sep 10, 2024
- 272
- 281
- 253
- 267
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D): 267.
a2 + b2 = 89........ (1)
a2 - b2= 39........ (2)
From (1) and (2):
a2 = 64 => a = 8
b2 = 25 => b = 5
Now,
a3 - b3 - 3ab
= 83 - 53 - 3 * 8 * 5
= 512 - 125 – 120
= 267.
a2 + b2 = 89........ (1)
a2 - b2= 39........ (2)
From (1) and (2):
a2 = 64 => a = 8
b2 = 25 => b = 5
Now,
a3 - b3 - 3ab
= 83 - 53 - 3 * 8 * 5
= 512 - 125 – 120
= 267.
Was this answer helpful?
0
0
Top Questions on Basic Algebra
- For every 2 boy students there are 3 girl students and for every 4 male teacher there are 5 female teachers. If the ratio of number of teachers to the number of students is 1:10, then which of the following is the ratio of the number of boy students to the number of male teachers?
- ATMA - 2021
- Quantitative Aptitude
- Basic Algebra
- A certain number of cakes is distributed equally among Alex, Bruce, Clive and Daniel. Alex gives away \((\frac{3}{4})^{th}\) of his cakes equally among the other three people. Later Bruce gives half of his cakes to Daniel. What fraction of the total number of cakes does Daniel have in the end?
- ATMA - 2021
- Quantitative Aptitude
- Basic Algebra
- Investment of ₹ 4,000 at \(R\%\) per annum compounded annually becomes 16,000 in 8 years. If 2,000 is invested at \(R\%\) per annum compounded annually, then in how many years will the investment become 16,000?
- ATMA - 2021
- Quantitative Aptitude
- Basic Algebra
- A rabbit on a controlled diet is fed a total of 1 kg of carrot every day. There are 2 types of carrots that are fed to the rabbit. Type X carrot contains \(60\%\) protein and type Y carrot contains \(80\%\) protein. If the rabbit must be fed 650 grams of protein everyday, then how many grams of type X carrot must be fed to the rabbit?
- ATMA - 2021
- Quantitative Aptitude
- Basic Algebra
- In a certain manufacturing plant, the ratio of the number of workers to managers is 7: 2. The total number of employees which consists of workers and managers only is 45,000. The manufacturing plant plans to hire new employees such that for every five workers there is a manager. How many new workers should the manufacturing plant hire?
- ATMA - 2021
- Quantitative Aptitude
- Basic Algebra
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
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
View More Questions