Question

解下列方程

t²-t=2
x²-6x=7
x²-3=-3x

Answer 1

t²-t=2
t^2-t-2=0
(t-2)(t+1)=0
t1=2, t2=-1

x²-6x=7
x^2-6x-7=0
(x-7)(x+1)=0
x1=7, x2=-1

x²-3=-3x
x^2+3x-3=0
a=1, b=3,c=-3
b^2-4ac=9+12=21
x=(-3±√21)/2
x1=(-3+√21)/2, x2=(-3-√21)/2

Answer 2

t²-t=2
t²-t+1/4=9/4
(t-1/2)²=9/4
t-1/2=3/2 t-1/2=-3/2
∴t=2 或t=-1

x²-6x=7
x²-6x+9=16
(x-3)²=16
∴x-3=4 x-3=-4
∴x=7 x=-1

x²-3=-3x
x²+3x=3
x²+3x+9/4=21/4
(x+3/2)²=21/4
x+3/2=- √21/2 x+3/2=√21/2
∴x=-3/2-√21/2 x=-3/2+√21/2