Question 1145557
125+x=y^2
176+x=z^2
z^2-y^2=51
x=y^2-125
x=z^2-176
y^2-125=z^2-176
z^2-y^2=176-125
z^2-y^2-51

The 2 squares differ by 51

We can solve it logically and using trial and error.
13^2 169
so z^2 must be at 14
30^2 =900
29^2= 841
which differ by 59
so y^2 must be less 30 and more than 14
 
30 900
29 841
30 ^2 -29^2=59
900 -841=59 too much
20^2-19^2=
400-361=39 too small
59-39=20
Let's try half way
26 676
25 625
676-625=51
so x=25 y =26
625-125=500
676-176=500
x=500