Question
If 343x3 - 27y3 = (7x - Ay) X
(Bx2 + y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.Solution
343x3 - 27y3 = (7x - Ay) X (Bx2 + y2 + Cxy) We know that, a3 - b3 = (a - b) X (a2 + b2 + ab) So, 343x3 - 27y3 = (7x)3 - (3y)3 = (7x - 3y) X (49x2 + 9y2 + 7x X 3y) = (7x - 3y) X (49x2 + 9y2 + 21xy) So, (7x - Ay) X (Bx2 + y2 + Cxy) = (7x - 3y) X (49x2 + 9y2 + 21xy) On comparing coefficients of LHS and RHS, we get, A = 3, B = 49, and C = 21 So, 3 X (2A + 6B) - 2C = 3 X {2 X 3 + 6 X 49} - 2 X 21 = 3 X (6 + 294) - 42 = 3 X 300 - 42 = 900 - 42 = 858
Four numbers are arranged in ascending order. When the 1st two numbers are increased by the number equal to their position, and the last two numbers (i....
The average salary of a group of 12 employees is Rs. 60,000. When one employee departs, the average salary of the remaining 11 employees drops by Rs. 2,...
Average marks scored by Vineet in five subjects are 85. The average marks scored by him (excluding his highest and lowest marks) are 65 and lowest marks...
The average of 7 numbers is 32. If one number 28 is removed, what is the approximate average of the remaining 6 numbers?
The average age of a group of persons going for tour to Shimla is 22 years. 30 new persons with an average age of 8 years join the group and their avera...
- Rs. 4200 was distributed among 'P', 'Q', 'R' and 'S' in the ratio 2:5:4:3 respectively. Later, 'Q' gave an amount equal to 80% of the average amount receiv...
A is 75% more than B. C is 60 less than A. Average of A, B and C is 340. The ratio of B and C is 2:x. Find the value of x.
The average expenditure of a man for the first 4 month is Rs.5000 and for the next 8 months is Rs.8000. If he saves 12000 in that year then find his ave...
The average price of two mobile phones, namely 'P' and 'Q' is Rs. 15,600 whereas the average price of phones 'Q' and 'R' is Rs. 1...
The average score of 50 students in an exam is 68. If the average of 30 boys is 72, what is the average score of the girls?
Relevant for Exams:
