The sum of two numbers is 1000 and the difference between their squares is 256000.Find the numbers.
Answers
Given : The sum of two numbers is 1000 and the difference between their squares is 256000.Find the numbers.
Solution:
Let the numbers are x and y.
ATQ :
Condition : 1
x + y = 1000 ………...(1)
Condition : 2
x² – y² = 256000
(x + y)(x - y) = 256000
[a² - b² = (a + b) (a - b)
1000(x - y) = 256000
[From eq 1]
x - y = 256000/1000
x - y = 256 ………….(2)
On adding equations (1) and (2) :
x + y = 1000
x - y = 256
------------------
2x = 1256
x = 1256/2
x = 628
On putting x = 628 in eq (1) we obtain :
x + y = 1000
628 + y = 1000
y = 1000 - 628
y = 372
Hence, the numbers are 628 and 372.
Hope this answer will help you…
Some more questions from this chapter :
The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.
https://brainly.in/question/17175907
The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number. How many such numbers are there?
https://brainly.in/question/17176636
Step-by-step explanation:
x= 628
y= 372
hope it helps
