Question
The cube of the difference between two given natural
numbers is 1000, while the product of these two given numbers is 56. Find the positive difference between the cubes of these two given numbers.Solution
1st natural number = x 2nd natural number = y (x - y)3 = 1000 (x - y) = 3√1000 = 10 … (1) squaring both sides (x - y) ² = 100 x2+y2-2xy =100 x² + y² = 100 + 112 = 212 Now, (x + y) = √ (x² + y² + 2xy) =√ (212 + 112) = √324 = 18 … (2) Now Eq (1) +Eq (2). x-y+x+y =10+18=28 2x =28 x=14 y=4 Now positive difference between the cubes= (14)3-(4)3 =2744-64 =2680.
Where is Nanda Devi Mountain?
What is the salt measurement in hypersaline lagoons?
Which of these state governments has implemented PESA act in November 2022?
Which of the following has four chambered heart?
The highest surcharge rate of 37% on income above 5 crores shall be reduced to ______ % under the new tax regime?
Which type of mirror is used by dentists to see large images of patients' teeth?
Asexual reproduction takes place through budding in-
Which Article of the Indian Constitution, under The Right of Children to Free and Compulsory Education Act or Right to Education Act (RTE), describes t...
What percentage of India's total monthly crude oil demand is currently being fulfilled by Russia?
Which Indian state is using drone technology and a digital platform to revive the PM-KUSUM programme?