+128473 1/a + 1/b = 1/34
Let z = 34
And a =z + m
And b = z + n
So we have
1/ ( z + m) + 1/ (z + n) = 1 /z
( 2z+ m + n) / [ (z + m) ( z + n) ] = 1 / z cross-multiply
(2z + m + n) z = ( z + m) ( z + n) simplify
2z^2 + mz + nz = z^2 + mz + nz + mn
z^2 = mn
So
34^2 = mn =1156
2^2 * 17^2 = mn
2 * 2 * 17 * 17 = mn
a = 34 + m
b = 34 + n
m n a b
1 1152 35 1190
2 578 36 612
4 289 38 323
17 68 51 102
34 34 68 68
We can stop here
Depending on our choice for a, b
(a , b) = (35, 1190) ( 36 , 612) (38, 323) (51, 102) ( 68, 68)
