[tex]x^2-y^2=|(x+y)(x-y)| \\(x-y)^2= {x^2-2xy+y^2} ---->(1) \\(x+y)^2=x^2+2xy+y^2 \\x^2+y^2=(15)^2-2(54)=117 \\Subsitute (x^2+y^2) in equn (1), therefore (x-y)= \sqrt{117-2(54)}=\sqrt{9} \\Thus (x-y)=(+)or(-)3 \\Putting the values: x^2-y^2=(15)(3)=45[/tex]
