1.a+1/a=3,则a^2+1/a^2=( ).

题目

1.a+1/a=3,则a^2+1/a^2=( ).
A.7 B.9 C.10 D.11
2.若x+y=2,x^2+y^2=15,求xy的值.
3.若(x+y)^2=7,(x-y)^2=5,求xy的值.
4.若M=10a^2+2b^2-7a+6,N=a^2+2b^2+5a+1,试比较M和N的大小．
5．解方程：(3x+1)^2-(2x-1)^2=(x-1)(5x+2)-24.

答案

1.A
a+1/a=3,(a+1/a)^2=9即a^2+2+(1/a)^2=9
所以a^2 + 1/a^2 = 7
2.x+y=2
(x+y)^2=4
x^2+2xy+y^2=4
其中x^2+y^2=15
所以2xy=4-15=-9
xy=-4.5
3.(x+y)^2=7
x^2 + 2xy + y^2=7 (1)
(x-y)^2=9
x^2 - 2xy + y^2=9 (2)
(1)-(2)得：4xy=-2
xy=-0.5
4.M-N=9a^2+12a+5=(3a+2)^2 + 1 >0
所以M>N
5．解方程：(3x+1)^2-(2x-1)^2=(x-1)(5x+2)-24
(9x^2+6x+1)-(4x^2-4x+1)=(5x^2-3x-2)-24
9x^2+6x+1-4x^2+4x-1=5x^2-3x-26
(9x^2-4x^2-5x^2)+6x+4x+3x=-26-1
13x=-27
x=-27/13