Question

三道数学题目

1.若x+y= -6,xy=2.75,则x-y=?
2.若x²+mx-15=(x+3)(x+n),则m的值为几？
3.(2+1)(2²+1)(2^4+1）......（2^2n)的值为多少?

Answer 1

1.(x+y)^2=36
x^2+y^2+2xy=36
x^2+y^2=36-2*2.75=30.5

(x-y)^2=x^2+y^2-2xy=30.5-2*2.75=25
x-y=5或者-5
2.m=-2
n=-5

3.(2+1)(2^2+1)(2^4+1).....(2^2n+1)
=（2-1）(2+1)(2^2+1)(2^4+1).....(2^2n+1)
=2^4n-1

Answer 2

解：由题可知
1.(x+y)^2=36
x^2+y^2+2xy=36
x^2+y^2=36-2*2.75=30.5
(x-y)^2=x^2+y^2-2xy=30.5-2*2.75=25
x-y=5或者-5
2.m=-2
n=-5
3.(2+1)(2^2+1)(2^4+1).....(2^2n+1)
=（2-1）(2+1)(2^2+1)(2^4+1).....(2^2n+1)
=2^4n-1