Question

知道的快说啊！！！已知a=根号7+根号3，b=根号7-根号3，求a的平方分之1+b的平方分之1 等于？？？？

Answer 1

a的平方分之1+b的平方分之1
=1/(√7+√3)²+1/(√7-√3)²
=1/(10+2√21)+1/(10-2√21)
=(10-2√21+10+2√21)/(100-4*21)
=20/16
=5/4

追问

1/(√7+√3)²+1/(√7-√3)²
怎么到这一步的..？？？具体一点说..谢了啊
1/(10+2√21)+1/(10-2√21)

追答

(√7+√3)²=(√7)²+2√7*√3+(√3)²
=7+2*√(7*3)+3
=10+2√21
(√7-√3)²=(√7)²-2√7*√3+(√3)²
=7-2*√(7*3)+3
=10-2√21

Answer 2

1.25

Answer 3

5/4

Answer 4

1/a^2+1/b^2
=(1/a+1/b)^2-2/ab
=[1/（根号7+根号3)+1/(根号7-根号3)]^2-2/(7-3)
=[(根号7-根号3+根号7+根号3)/(7-3)]^2-1/2
=(根号7/2)^2-1/2
=7/4-1/2=5/4