若x=1⼀2（根号3a+5b+根号3a-5b），y=1⼀2（根号3a+5b-根号3a-5b），求x的平方+xy+y的平方的值

x=1/2（根号3a+5b+根号3a-5b)=3a
y=1/2（根号3a+5b-根号3a+5b）=5b (这里改为+号，否则=0)
x的平方+xy+y的平方=(3a)^2+(3a)*(5b)+(5b)^2
=9a^2+15ab+25b^2

x^2+xy+y^2
=(x^2+2xy+y^2)-xy
=(x+y)^2-xy
=[根号3a+5b]^2-1/4*(根号3a+5b+根号3a-5b)(根号3a+5b-根号3a-5b)
=3a+5b-1/4[(3a+5b)-(3a-5b)]
=3a+5b-5b/2
=3a+5b/2

我觉得，你应该这样，根号3a+5b根号3a-5b，当做m½＋n½，x＝1／2﹙√m＋√n﹚，y＝1／2﹙√m－√n﹚，x＋y＝√m，xy＝1／4﹙m－n﹚，[﹙x＋y﹚＋xy]²＝﹙x＋y﹚²＋﹙xy﹚²＋2xy﹙x＋y﹚＝m﹢1／16﹙m－n﹚²＋1／2﹙m－n）√m，带入

x=1/{2[√(3a+5b)+√(3a-5b)]}=[√(3a+5b)-√(3a-5b)]/(12a) 分子分母同时乘以√(3a+5b)-√(3a-5b)
同理：y=1/{2[√(3a+5b)-√(3a-5b)]}=[√(3a+5b)+√(3a-5b)]/(12a)
x+y=√(3a+5b)/(6a)
xy=5b/(72a^2)
x^2+xy+y^2
=(x^2+2xy+y^2)-xy
=(x+y)^2-xy
=[√(3a+5b)/(6a)]^2-5b/(72a^2)
=(3a+5b)/(36a^2)-5b/(72a^2)
=(6a+10b-5b)/(72a^2)
=(6a+5b)/(72a^2)