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b分之根号b

Answer 1

a=2+√3
b=2-√3
ab=(2+√3)(2-√3)=1
(√a+√b)²=(2+√3+2-√3)²=4²=16
(√a+√b)=4
(√a-√b)²=(2+√3-2+√3)²=(2√3)²
(√a-√b)=2√3

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

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追答

a=2+√3
b=2-√3
ab=(2+√3)(2-√3)=1
a²=7+4√3
b²=7-4√3
a/(a-√ab)
=a/(a-1)
=(2+√3)/[(2+√3)-1]
=(2+√3)/(1+√3)
=(2+√3)(1-√3)/(1+√3)
=-1
√b/√(a+√b)
=[√b√(a+√b)]/(a+√b)
=[√ab+b√b]/(a+√b)
=[1+b√b]/(a+√b)
=[1+b√b](a-√b)/(a²-b)
=(a+ab√b-b√b-b²)/(a²-b)
=(a-b²)/(a²-b)
=(2+√3-7+4√3)/(7+4√3-2+√3)
=5(-1+√3)/5(1-√3)
=(-1+√3)/(1-√3)
=-(1-√3)/(1-√3)
=-1
∴a/(a-√ab)-√b/√(a+√b)=（-1）-（-1）=0