Question 37808
Let the integers be x and y
x+y=25
y=25-x (subsitution)
{{{x^2-y^2=275}}}
Subsitute for y:
{{{x^2-(25-x)^2=275}}}
{{{x^2-(625+x^2-50x)=275}}}
{{{50x-900=0}}}
x=18
y=25-18
y=7
Hence, the two integers are 18 and 7.
Paul.