Question
If 2x + 4y - 9 = 0, then find the value of 8x 3
- 723 + 64y 3 + 216xy.Solution
2x + 4y - 9 = 0
If, a + b - c = 0, then, a 3 + b 3 - c 3 = - 3abc
So, (2x) 3 + (4y) 3 + ( - 9) 3 = - 3 X (2x) X (4y) X (9)
Or, 8x 3 + 64y 3 - 729 = - 216xy
Or, 8x 3 + 64y 3 - 729 + 216xy = 0 ....(i)
8x 3 - 723 + 64y 3 + 216xy = 8x 3 - 729 + 6 + 64y 3 + 216xy
Put the value of equation (i) in the above equation, we get,
8x 3 - 723 + 64y 3 + 216xy = 0 + 6 = 6
Gaurav covered 225 km distance in 9 hours. The first part of his journey he covered by car, then he hired a rickshaw. The speed of car and rickshaw is 3...
A man travels some distance at a speed of 20 km/hr and returns at a speed of 15 km/hr. If the total time taken by him is 2 hrs 20 min, the distance is <...
Ajay and Vishal left the place ‘X’ with different speeds which are in the ratio 9:4 respectively. Ajay left the place 30 seconds after Vishal. If af...
Raman traveled a certain distance at a particular speed. If he had traveled 6 km/h faster, he would have taken 30 minutes less. If he had traveled 5 km/...
A was travelling from point X to point Y. He increased his speed by 20 km/h after every hour. He reached his destination in 14 hours. If his initial spe...
- A cyclist starts chasing a biker who is 1,200 metres ahead. The cyclist rides at 24 m/s, and the biker is going at 16 m/s. Find the time taken by the cycli...
A swimmer swims from point X upstream for 4 minutes. Then he turns and swims downstream for 4 minutes and reaches point Y. If the distance between X and...
Average speed of ‘A’ during a 24-hour journey is 32 km/h. If he covered the first 160 km of his journey at a speed of 20 km/h, then find the speed a...
A boy is traveling to a destination. If he moves at a speed of 20 meters per second, he arrives 20 seconds late. Conversely, if his speed is 40 meters p...
A train covers a certain distance at a speed of 48 km/h and the next same distance with a speed of 60 km/h and the next same distance with a speed of 80...
Relevant for Exams:
