國中數學,請大家幫幫忙急需!!!(附算式) 1. a+b=7,ab=3則b/a+a/b=______ 2. x-1/x=-2/3,x>0則 (1) (x+1/x)平方=______ (2) x平方+1/x平方=______?

1. a+b=7,ab=3則b/a+a/b=______
Sol
a^2+b^2=(a+b)^2－2ab=49－6=43
b/a+a/b
=b^2/(ab)+a^2/(ab)
=(a^2+b^2)/(ab)
=43/3
2. x-1/x=-2/3,x>0則
(1) (x+1/x)^2
=x^2+2+1/x^2
=x^3－2+1/x^2+4
=(x－1/x)^2+4
=4/9+4
=40/9
(2) x^2+1/x^2
=x^2－2+1/x^2+2
=(x－1/x)^2+2
=4/9+2
=22/9

I will only provide the steps instead of the actual value, so that you actually put some effort in it.

Q1:
b/a+a/b=(a^2+b^2)/(ab)=[(a+b)^2-2ab]/(ab)

Q2 (1):
(x+1/x)^2=x^2+1/x^2+2=(x-1/x)^2+4

Q2 (2):
Similar to Q2(1)