Question

x^2+y^2=6,xy=2 .Чему ровно x^4+x^2y^2+y^4?

Answer 1

$x^2+y^2=6; ,; ; ; xy=2\\\6^2=(x^2+y^2)^2=x^4+2x^2y^2+y^4\\x^4+2(xy)^2+y^4=36\\x^4+2cdot 2^2+y^4=36\\x^4+y^4=36-8\\x^4+y^4=28\\\x^4+x^2y^2+y^4=(x^4+y^4)+(xy)^2=28 +2^2=32$