1.已知x-1/x=4,求x^2+1/x^2的值.
（x-1/x)²=16
x²+1/x²-2=16
所以x^2+1/x^2=16+2=18
2.已知x+y=4,x-y=10,求xy的值.
（x+y)²=x²+y²+2xy=16
(x-y)²=x²+y²-2xy=100
所以4xy=-84
xy=-21
3.(a+2b)(a-2b)(a^2+4b^2)
=(a²-4b²)(a²+4b²)
=a^4-16b^4
4.先化简,再求值(-b+a)(a+b)+(a+b)^2-2a^2,其中a=3,b=1/4.
(-b+a)(a+b)+(a+b)^2-2a^2
=a²-b²+a²+b²+2ab-2a²
=2ab
=2*3*1/4
=3/2
5.12346^2-12345x12347
=12346²-(12346-1)*(12346+1)
=12346²-12346²+1
=1
6.2007^2-4014X2008+2008^2
=2007²-2*2007*2008+2008²
=(2007-2008)²
=1
7.(2+1)(2^2+1)(2^4+1)…[2^2^n+1]
=(2^2^n)+1)(2^2^n-1)
=4^2^n-1
=16^n-1