Question 909164
(x+y)(x^2+y^2)=65

x(x^2+y^2)+y(x^2+y^2)=65

x^3+xy^2+x^2y+y^3=65..................(1)

(x-y)(x^2-y^2)=5

x(x^2-y^2)-y(x^2-y^2)=5

x^3-xy^2-x^2y+y^3=5.....................(2)

add (1) & (2)

2x^3+2y^3=70

x^3+y^3=35.........................(3)

subtract (2) from (1)

2x^2y+2xy^2=60
2xy(x+y)=60
xy(x+y)=30

from (3)
x^3+y^3=35.........................(3)

(x+y)^3-3xy(x+y)=35

(x+y)^3+3(30)=35

(x+y)^3=90+35

(x+y)^3=125
(x+y)=5...........................(4)

Now we know
(x-y)(x^2-y^2)=5

(x-y)(x+y)(x-y)=5
(x+y)(x-y)^2=5

5(x-y)^2=5

(x-y)^2=5/5=1

x-y=+/-1...................................(5)

solve (4)&(5) 


we have (2,3) OR (3,2) as the solutions