Question

已知a=4+2根号3,b=4-2根号3,求(a+1/b)(b+1/a)的值

Answer 1

(a+1/b)(b+1/a)
=(ab+1)/b * (ab+1)/a
=(ab+1)^2/ab
ab=(4+2√3)*(4-2√3)
=16-12
=4
所以原式=(4+1)^2/4
=25/4

追问

=(ab+1)/b * (ab+1)/a
这里为什么要除个b，a呢

追答

通分了
a+1/b=(ab+1)/b
b+1/a=(ab+1)/a

直接打开括号相乘也可以

Answer 2

(a+1/b)(b+1/a)
=(4+2√3+1)/(4-2√3)×(4-2√3+1)/(4+2√3)
=(5+2√3)(5-2√3)/(4-2√3)(4+2√3)
=(25-12)/(16-12)
=13/4

Answer 3

(a+1/b)(b+1/a)=ab+1+1+1/ab=ab+1/ab+2
a=4+2跟号3
b=4-2跟号3
ab=(4+2跟号3)(4+2跟号3)=16-12=4
ab+1/ab+2=4+1/4+2=6.25

Answer 4

25/4