[tex](x+y)^2+(x-y)^2=10[/tex]
[tex]\implies 2x^2+2y^2=10[/tex]
[tex]\implies x^2+y^2=5[/tex]
[tex]\implies (x^2+y^2)^2=x^4+2x^2y^2+y^4=25[/tex]
[tex](x+y)^4+(x-y)^4=98[/tex]
[tex]\implies 2x^4+12x^2y^2+2y^4=98[/tex]
[tex]\implies x^4+6x^2y^2+y^4=49[/tex]
[tex]\implies 25+4x^2y^2=49[/tex]
[tex]4x^2y^2=24[/tex]
[tex]\implies x^2y^2=6[/tex]
[tex]\implies xy=\sqrt6[/tex]
