Question

x³+y³+15xy-125ifx+y=5

Answer 1

x^3+y^3 +15xy -125 

(using X^3+y^3 = (x+y)(x^2-xy+y^2) ) 

(x+y)(x^2-xy+y^2)+ 15xy -125 
since x+y = 5 

5(x^2-xy+y^2)+ 15 xy -125 
5 x^2 - 5xy +5y^2 +15xy -125 

5x^2 + 10 xy + 5y^2 -125 

5(X^2 + 2xy + y^2)-125 
5(x+y)^2 -125 
5(5)^2 -125 

5(25) -125 
125 -125 
0

Answer 2

we can solve it as below

=x^3+y^3+15xy-125+3xy(x+y)-3xy(x+y) by adding and subtracting 3xy(x+y) 
so we can write x^3+y^3+3xy(x+y) =(x+y)^3 
and the equation becomes 
=(x+y)^3+15xy-125-3xy(x+y) 

now substitute x+y=5 in the above equation 

=5^3 +15xy-125-3xy*5 
now 5^3=125 
3xy*5=15xy 
thus equation becomes 
=125+15xy-125-15xy 
=0 


thus the answer is zero