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a) \(\left(4x-1\right)-\left(4x+1\right)\left(x-2\right)=12\)
\(\Leftrightarrow4x-1-\left(4x^2-7x-2\right)=12\)
\(\Leftrightarrow4x-1-4x^2+7x+2=12\)
\(\Leftrightarrow4x^2-11x+11=0\)( Pt vô nghiệm )
b) \(\left(2x-3\right)\left(2x+1\right)-\left(2x-2\right)^2=15\)
\(\Leftrightarrow\left(4x^2-4x-3\right)-\left(4x^2-8x+4\right)=15\)
\(\Leftrightarrow4x=22\)
\(\Leftrightarrow x=\frac{11}{2}\)
(4x - 1) - (4x + 1)(x - 2) = 12
=> 4x - 1 - 4x2 - 7x - 2 = 12
=> (4x - 7x) + (- 1 - 2) - 4x2 = 12
=> -3x - 3 - 4x2 = 12
=> -3x - 4x2 = 15
=> không tồn tại x
b. (2x - 3)(2x + 1) - (2x - 2)(2x - 2) = 15
=> 2x(2x + 1) - 3(2x + 1) - 2x(2x - 2) + 2(2x - 2) = 15
=> 4x2 + 2x - 6x - 3 - 4x2 + 4x - 4x - 4 = 15
=> (4x2 - 4x2) + (2x - 6x + 4x - 4x) + (-3 - 4) = 15
=> -4x - 7 = 15
=> -4x = 22
=> x = \(-\frac{11}{2}\)
a, \(\left(4x-1\right)-\left(4x+1\right)\left(x-2\right)=12\)
\(\Leftrightarrow4x-1-4x^2+8x-x+2=12\)
\(\Leftrightarrow11x+1-4x^2=12\)
\(\Leftrightarrow11x-11-4x^2=0\)( vô nghiệm )
b, \(\left(2x-3\right)\left(2x+1\right)-\left(2x-2\right)^2=15\)
\(\Leftrightarrow4x^2+2x-6x-3-4x^2+8x-4=15\)
\(\Leftrightarrow4x-7=15\Leftrightarrow4x=22\Leftrightarrow x=\frac{11}{2}\)
1.a) 2x4-4x3+2x2
=2x2(x2-2x+1)
=2x2(x-1)2
b) 2x2-2xy+5x-5y
=2x(x-y)+5(x-y)
=(2x+5)(x-y)
2.
a) 4x(x-3)-x+3=0
=>4x(x-3)-(x-3)=0
=>(4x-1)(x-3)=0
=> 2 TH:
*4x-1=0 *x-3=0
=>4x=0+1 =>x=0+3
=>4x=1 =>x=3
=>x=1/4
vậy x=1/4 hoặc x=3
b) (2x-3)^2-(x+1)^2=0
=> (2x-3-x-1).(2x-3+x+1)=0
=>(x-4).(3x-2)=0
=> 2 TH
*x-4=0
=> x=0+4
=> x=4
*3x-2=0
=>3x=0-2
=>3x=-2
=>x=-2/3
vậy x=4 hoặc x=-2/3
Rút gọn hết ta được :
a/ 41x - 17 = -21
=> 41x = -4 => x = 4/41
b/ 34x - 17 = 0
=> 34x = 17
=> x = 17/34 = 1/2
c/ 19x + 56 = 52
=> 19x = -4
=> x = -4/19
d/ 20x2 - 16x - 34 = 10x2 + 3x - 34
=> 10x2 - 19x = 0
=> x(10x - 19) = 0
=> x = 0
hoặc 10x - 19 = 0 => 10x = 19 => x = 19/10
Vậy x = 0 ; x = 19/10
Rút gọn hết ta được :
a/ 41x - 17 = -21
=> 41x = -4 => x = 4/41
b/ 34x - 17 = 0
=> 34x = 17
=> x = 17/34 = 1/2
c/ 19x + 56 = 52
=> 19x = -4
=> x = -4/19
d/ 20x 2 - 16x - 34 = 10x 2 + 3x - 34
=> 10x 2 - 19x = 0
=> x(10x - 19) = 0
=> x = 0 hoặc 10x - 19 = 0
=> 10x = 19
=> x = 19/10
Vậy x = 0 ; x = 19/10
a, \(\left(x+3\right)^3-\left(x+2\right)\left(x-2\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-\left(x^2-4\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-x^2+4+6x^2+20\)
\(=x^3+14x^2+27x+51\)
b, \(\left(2x+3\right)\left(4x^2-6x+9\right)-\left(2x-3\right)\left(4x^2+6x+9\right)\)
\(=8x^3-12x^2+18x+12x^2-18x+18-\left(8x^3+12x^2+18x-12x^2-18x-18\right)\)
\(=8x^3+18-8x^3+18=36\)
c, \(\left(2x-1\right)\left(4x^2+2x+1\right)\left(2x+1\right)\left(4x^2-2x+1\right)\)
\(=\left(8x^3+4x^2+2x-4x^2-2x-1\right)\left(8x^3-4x^2+2x+4x^2-2x+1\right)\)
\(=\left(8x^3-1\right)\left(8x^3+1\right)=\left(8x^3\right)^2-1\)
\(=64x^5-1\)
d, \(\left(x+4\right)\left(x^2-4x+16\right)-\left(50+x^2\right)\)
\(=x^3-4x^2+16x+4x^2-16x+64-50-x^2\)
\(=x^3-x^2+14\)
Chúc bạn học tốt!!!
a.\(\left(4x-1\right)-\left(4x+1\right).\left(x-2\right)=12\)
\(\Leftrightarrow4x-1-\left(4x^2-7x-2\right)-12=0\)
\(\Leftrightarrow4x-1-4x^2+7x+2-12=0\)
\(\Leftrightarrow-4x^2+11x-11=0\)
\(\Rightarrow4x^2-11x+11=0\)
\(\Leftrightarrow\left(2x\right)^2-2.2x.\frac{11}{4}+\frac{11^2}{4^2}-\frac{11^2}{4^2}+11=0\)
\(\Leftrightarrow\left(2x-\frac{11}{4}\right)^2+\frac{55}{16}=0\)( VÔ LÝ )
VẬY KHÔNG CÓ GIÁ TRỊ NÀO CỦA x THỎA MÃN PT ĐÃ CHO
b. \(\left(2x-3\right).\left(2x+1\right)-\left(2x-2\right)^2=15\)
\(\Leftrightarrow4x^2-4x-3-4x^2+8x-4-15=0\)
\(\Leftrightarrow4x-22=0\)\
\(\Leftrightarrow x=\frac{11}{2}\)
VẬY PT CÓ NGHIỆM x= 11/2