find all (x,y) where x, y are natural numbers such that (i) 1/x+1/y=1 (ii) xy + 5x = 4y + 38
Answers
Given : (i) 1/x+1/y=1 (ii) xy + 5x = 4y + 38 x, y are natural numbers
To find : find all possible (x,y)
Step-by-step explanation:
1/x+1/y=1
x = 1 then no value of y exist
x = 2 , y = 2 is only solution
( 2, 2)
xy + 5x = 4y + 38
x < 5 will not give any solution at 5x will be less than 38 and also xy ≤ 4y
x = 5
=> 5y + 25 = 4y + 38
=> y = 13
x = 5 , y = 13
x = 6
=> 6y + 30 = 4y + 38
=> 2y = 8
=> y = 4
=> x = 6 , y = 4
x = 7
=> 7y + 35 = 4y + 38
=> 3y = 3
=> y = 1
x = 7 , y = 1
x > 7 there will be no solution
as 7y > 4y & 5x > 38
(5 , 13) , (6 , 4) & (7 , 1) are possible solutions
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