Product is 4 times the sum
Number Theory
Level
3
How many pairs of integers are there such that their product equals 4 times their sum?
12
10
9
15
5
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1 solution
Ans: 10
x y x y − 4 x − 4 y x y − 4 x − 4 y + 1 6 ( x − 4 ) ( y − 4 ) And the possible answers are: = 4 ( x + y ) = 0 = 1 6 = 1 6
1 : 2 : 3 : 4 : 5 : 6 : 7 : 8 : 9 : 1 0 : ( x − 4 ) , ( y − 4 ) ( − 1 6 , − 1 ) ( − 8 , − 2 ) ( − 4 , − 4 ) ( − 2 , − 8 ) ( − 1 , − 1 6 ) ( 1 , 1 6 ) ( 2 , 8 ) ( 4 , 4 ) ( 8 , 2 ) ( 1 6 , 1 ) ( x , y ) ( − 1 2 , 3 ) ( − 4 , 2 ) ( 0 , 0 ) ( 2 , − 4 ) ( 3 , − 1 2 ) ( 5 , 2 0 ) ( 6 , 1 2 ) ( 8 , 8 ) ( 1 2 , 6 ) ( 2 0 , 5 )