1.x的平方+xy=13,xy+y的平方=12,求(x+y)(x-y)和(x+y)的平方的值.
x^2+xy=13
xy+y^2=12
两式相减有
x^2-y^2=1
即
(x+y)(x-y)=1
两式子相加有
x^2+2xy+y^2=25
(x+y)^2=25
2.计算
3(2的平方+1)(2的4次方+1)(2的8次方+1)+1=?
(2^2+1)(2^4+1)(2^8+1)+1
=(1/3)(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(1/3)(2^4-1)(2^4+1)(2^8+1)+1
=(1/3)(2^8-1)(2^8+1)+1
=(1/3)(2^16-1)+1
=(1/3)*65535+1
=21845+1
=21846