1、
(1)196x^2=1
==> x^2=1/196
==> x=±1/14
(2)4x^2+12x+9=81
==> (2x+3)^2=81
==> 2x+3=9,或者2x+3=-9
==> x=3,或者x=-6
(3)x^2-7x-1=0
所以,x=[7±√(49+4)]/2=(7±√53)/2
(4)2x^2+3x=3
==> 2x^2+3x-3=0
==> x=[-3±√(9+24)]/4=(-3±√33)/4
(5)x^2-2x+1=25
==> (x-1)^2=25
==> x-1=5,或者x-1=-5
==> x=6,或者x=-4
(6)x(2x-5)=4x-10
==> x(2x-5)=2(2x-5)
==> (x-2)(2x-5)=0
==> x=2,或者x=5/2
(7)x^2+5x+7=3x+11
==> x^2+2x=4
==> x^2+2x+1=5
==> (x+1)^2=5
==> x+1=±√5
==> x=-1±√5
(8)1-8x+16x^2=2-8x
==> 16x^2=1
==> x^2=1/16
==> x=±1/4
设一个数为a,另一个为8-a,则：a(8-a)=9.75
==> a^2-8a+9.75=0
==> 4a^2-32a+39=0
==> (2a-3)(2a-13)=0
==> a=1.5,或者a=6.5
则,8-a=6.5,或者8-a=1.5
即,这两个数为1.5和6.5
设长为a,宽就是a-3,依题意有：a(a-3)=4
==> a^2-3a-4=0
==> (a+1)(a-4)=0
==> a=-1＜0,舍去；或者a=4
所以,a-3=1
即,长为4,宽为1