Prove here!
are positive integers such that:
;
;
.
Then
= ?
The answer is 172.
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1 solution
The three equations may be written as
( 2 a + 5 ) ( 2 b + 5 ) = 2 0 9 = 1 1 ⋅ 1 9
( 2 b + 5 ) ( 2 c + 5 ) = 2 9 7 = 1 1 ⋅ 2 7
( 2 c + 5 ) ( 2 a + 5 ) = 5 1 3 = 1 9 ⋅ 2 7
which gives a = 7 , b = 3 , c = 1 1
and finally, 7 a + 8 b + 9 c = 1 7 2