Question

已知a=2+根号3,b=2-根号3,求a-根号ab分之a-根号a+根号ab分之根号b的值

Answer 1

a=2+√3，b=2-√3 ∴ab=﹙2+√3﹚﹙2-√3﹚=1，
a=½﹙4＋2√3﹚=½﹙√3＋1﹚²，∴√a=﹙√3＋1﹚／√2=½﹙√6＋√2﹚
b=½﹙4－2√3﹚=½﹙√3－1﹚²，∴√b=﹙√3－1﹚／√2=½﹙√6－√2﹚
a-根号ab分之a-根号a+根号ab分之根号b=a－a－√a＋√b
=√b－√a
=½﹙√6－√2﹚－½﹙√6＋√2﹚
=－√2

Answer 2

已知a=2+根号3,b=2-根号3,
ab=(2+根号3)(2-根号3)=2²-(根号3)²=4-3=1
根号ab=1;

a-根号ab分之a-根号a+根号ab分之根号b
=a-a-根号a+根号b
=-(2+根号3)+2-根号3,
=-2根号3

追问

（a-根号ab）分之a-（根号a+根号ab）分之根号b的值