Let x and y be positive integers such that x(x - y) = 8y-7. Find the value of X=Y
Answers
Given : x and y are positive integers
x(x - y) = 8y-7
To Find : Values of x and y
(x + y)/(x - y)
Solution:
x(x - y) = 8y-7
=> x² - xy = 8y - 7
=> x² + 7 = y(8 + x)
=> y = (x² + 7)/(x + 8)
=> y = (x² -64 + 71)/(x + 8)
=> y = (x² -64)/(x + 8) + 71/(x + 8)
=> y = x -8 + 71/(x + 8)
71 is a prime number
and x and y are positive integers
Hence x + 8 must be equal to 71 as x + 8 can not be 1
=> x + 8 = 71
=> x = 63
y = x -8 + 71/(x + 8)
= 63 - 8 + 1
= 56
x = 63
y = 56
x - y = 63 - 56 = 7
x + y = 63 + 56 = 119
(x + y)/(x - y) = 119/7 = 17
(x + y)/(x - y) = 17
x = 63 , y = 56
Learn More:
if x+y=5,y+z=7, z+x=6 then find the value of x, y, z - Brainly.in
brainly.in/question/7846545?source=aid16766256
9:12:18 = x:y:12 find the value of x and y in the given equation ...
brainly.in/question/1958824