The rest two unknown
If positive integers , and satisfy the equation above, then which of the following value is possible for ?
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1 solution
3 6 + 1 6 5 = a + b c
Squaring both sides gives us
( 3 6 + 1 6 5 ) 2 = ( a + b c ) 2
3 6 + 1 6 5 = a 2 + b 2 c + 2 a b c
Therefore,
a 2 + b 2 c = 3 6
2 a b = 1 6
c = 5
Since 2 a b = 1 6 , a b = 8 .
Finally, a b c = 4 0 .