用公式法接下列方程(1)x^2-5X=6(2)3X^2-11X-4=0(3)3x^2+10x+3=0(4)6t^2-13t-5=0(5)4x^2+9=12x(6)2/3x^2-1/6x-1/2=0(7)2x^2-根号2x-1=0(8)0.1y^2-y-0.2=0

Question

用公式法接下列方程
(1) x^2-5X=6
(2)3X^2-11X-4=0
(3)3x^2+10x+3=0
(4)6t^2-13t-5=0
(5)4x^2+9=12x
(6)2/3x^2-1/6x-1/2=0
(7)2x^2-根号2x-1=0
(8)0.1y^2-y-0.2=0

Answer 1

(1) x^2-5X=6
x^2-5x-6=0
(x-6)(x+1)=0
得 x=6 或x=-1
(2)3X^2-11X-4=0
(3x+1)(x-4)=0
得 x=-1/3 或 x=4
(3)3x^2+10x+3=0
(3x+1)(x+3)=0
得 x=-1/3 或x=-3
(4)6t^2-13t-5=0
(2t-5)(3t+1)=0
得 t=5/2 或 t=-1/3
(5)4x^2+9=12x
4x^2-12x+9=0
(2x-3)²=0
得 x=3/2
(6)2/3x^2-1/6x-1/2=0
4x^2-x-30
(4x+3)(x-1)=0
得 x=-3/4 或x=1
(7)2x^2-根号2x-1=0
(根号2x-1/2)^2=5/4
得 x=(根号2+根号10)/4
或 x=(根号2-根号10)/4
(8)0.1y^2-y-0.2=0
y^2-10y-2=0
y^2-10y+25=27
(y+5)^2=27
得 y=-5+3根号3
或 y=-5-3根号3