#### Question

Given positive even numbers x,y , if x^2y+xy^2=96 , find the value of x^2+y^2

Question

Given positive even numbers x,y , if x^2y+xy^2=96 , find the value of x^2+y^2

x^2y+xy^2

=xy(x+y)

=96

=2×2×24

=2×4×12

=4×4×6

=2×6×8 =2×6×(2+6)

\therefore x=2, y=6

x^2+y^2

=4+36

=40