急．．．1．求证：无论a,b为何值时,代数式a^2b^2-2ab+3的值均为正值.2．已知x+(x份之一）＝2,求x^3+(x^3份之一）的值．3．试证2^48-1可被63,65整除．

Question

急．．．
1．求证：无论a,b为何值时,代数式a^2b^2-2ab+3的值均为正值.
2．已知x+(x份之一）＝2,求x^3+(x^3份之一）的值．
3．试证2^48-1可被63,65整除．

Answer 1

1.) a^2b^2-2ab+3=(ab-1)^2+2所以,无论a,b为何值时,本式均为正值.2.) x+1/x=2则两边平方得:x^2+1/(x^2)=2两式相乘得:x^3+(x^3份之一）=23.) 2^48-1=(2^24+1)(2^24-1)=(2^24+1)(2^12+1)(2^12-1)=(2^24+1)(2^12+1)(2^6...