Bài 4:
a) (x-2)(x+5)-x²=2
⇔x²+5x-2x-10-x²=2
⇔3x-10=2
⇔3x=12
⇔x=4
b) (x+2)(x+3)-x(x+1)=6
⇔x²+3x+2x+6-x²-x=6
⇔4x=0
⇔x=0
c) 3x(4x-1)-(2x+1)(5+6x)=0
⇔12x²-3x-10x-12x²-5-6x=0
⇔ -18x-5=0
⇔ -18x =5
⇔ x= $\frac{-5}{18}$
d) (x+3)(2x-1)-(x-4)(2x+1)=10
⇔2x²-x+6x-3-2x²-x+8x+4=10
⇔12x+4=10
⇔12x=6
⇔x=$\frac{1}{2}$
e) 3(x-2)(x+2)-3x²+x=0
⇔3(x²-4)-3x²+x=0
⇔3x²-12-3x²+x=0
⇔ -12+x=0
⇔x=12
f) 2(x²-x)-2(x-1)(x+1)=4
⇔2x²-2x-2(x²-1)=4
⇔2x²-2x-2x²+2=4
⇔-2x+2=4
⇔ -2x=2
⇔x= -1
Bài 2:
a) -2x(x-5)+2(x-2)(x+2)-9x-2026
= -2x²+10x+2(x²-4)-9x-2026
= -2x²+10x+2x²-8-9x-2026
=x-2018
Thay x=2018 vào biểu thức ta có:
2018-2018=0
b) 3x(x-2)-(x+2)(x-8)
=3x²-6x-(x²-8x+2x-16)
=3x²-6x-x²+8x-2x+16
=2x²+16
Thay x= -2 vào biểu thức:
2.(-2)²+16=2.4+16=8+16=24
c) (x-1)(2x+1)-(x-1)(2x-3)
=2x²+x-2x-1-(2x²-3x-2x+3)
=2x²+x-2x-1-2x²+3x+2x-3
=4x-4
Thay x=$\frac{1}{4}$ vào biểu thức:
4.$\frac{1}{4}$ -4=1-4=-3
