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a)Dat \(x^2-4x+3=a;x^2-7x+6=b \Rightarrow a+b=2x^2-11x+9\)
....
\(b,\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\) \(\Leftrightarrow4x^2-4x+1+x^2+6x+9-5x^2+245=0\)\(\Leftrightarrow2x=-255\Rightarrow x=-\dfrac{255}{2}\)
\(c,\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)\(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6x^2+12x+6-49=0\)\(\Leftrightarrow24x=-13\Rightarrow x=-\dfrac{13}{24}\)
\(d,\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)
\(\Leftrightarrow x^3+8-x^3-2x=15\)
\(\Leftrightarrow-2x=23\Rightarrow x=-\dfrac{23}{2}\)
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)
b)(x2+x+1)(x2+x+2)-12
Đặt t=x2+x+1
t(t+1)-12=t2+t-12
=(t-3)(t+4)=(x2+x+1-3)(x2+x+1+4)
=(x2+x-2)(x2+x+5)
=(x-1)(x+2)(x2+x+5)
c)(x2+8x+7)(x2+8x+15)+15
Đặt t=x2+8x+7
t(t+8)+15=t2+8t+15
=(t+3)(t+5)
=(x2+8x+7+3)(x2+8x+7+15)
=(x2+8x+10)(x2+8x+22)
d)(x+2)(x+3)(x+4)(x+5)-24
=(x2+7x+10)(x2+7x+12)-24
Đặt t=x2+7x+10
t(t+2)-24=(t-4)(t+6)
=(x2+7x+10-4)(x2+7x+10+6)
=(x2+7x+6)(x2+7x+16)
=(x+1)(x+6)(x2+7x+16)
a/ Đặt x2 + 4x + 8 = a
Thì đa thức ban đầu thành
a2 + 3ax + 2x2 = (a2 + 2ax + x2) + (ax + x2)
= (a + x)2 + x(a + x) = (a + x)(a + 2x)
1, \(-4x\left(x-7\right)+4x\left(x^2-5\right)=28x^2-13\)
\(\Leftrightarrow-4x^2+28x+4x^3-20x=28x^2-13\)
\(\Leftrightarrow-32x^2+8x+4x^3-13=0\)( vô nghiệm )
2, \(\left(4x^2-5x\right)\left(3x+2\right)-7x\left(x+5\right)=\left(-4+x\right)\left(-2x+3\right)+12x^3+2x^2\)
\(\Leftrightarrow12x^3-7x^2-10x-7x^2-35x=-2x^2+11x-12+12x^3+2x^2\)
\(\Leftrightarrow12x^3-14x^2-45x=11x-12+12x^3\)
\(\Leftrightarrow-14x^2-56x-12=0\)( vô nghiệm )
Mình làm riêng ra nhá , chứ nhiều quá nên thông cảm cho mình :))
1. \(-4x\left(x-7\right)+4x\left(x^2-5\right)=28x^2-13\)
=> \(-4x^2+28x+4x^3-20x=28x^2-13\)
=> \(-4x^2+4x^3+\left(28x-20x\right)=28x^2-13\)
=> \(-4x^2+4x^3+8x-28x^2+13=0\)
=> \(\left(-4x^2-28x^2\right)+4x^3+8x+13=0\)
=> \(-32x^2+4x^3+8x+13=0\)
=> vô nghiệm
2. \(\left(4x^2-5x\right)\left(3x+2\right)-7x\left(x+5\right)=\left(-4+x\right)\left(-2x+3\right)+12x^3+2x^2\)
=> \(4x^2\left(3x+2\right)-5x\left(3x+2\right)-7x\left(x+5\right)=-4\left(-2x+3\right)+x\left(-2x+3\right)+12x^3+2x^2\)
=> \(12x^3+8x^2-15x^2-10x-7x^2-35x=8x-12-2x^2+3x+12x^3+2x^2\)
=> \(12x^3+8x^2-15x^2-10x-7x^2-35x-8x+12+2x^2-3x-12x^3-2x^2=0\)
=> \(\left(12x^3-12x^3\right)+\left(8x^2-15x^2-7x^2+2x^2-2x^2\right)+\left(-10x-35x-8x-3x\right)+12=0\)
=> \(-14x^2-56x+12=0\)
=> .... tự tìm
Câu c dấu bằng chỗ nào ?
a)
\((x+2)(x+4)(x+6)(x+8)+16\)
\(=[(x+2)(x+8)][(x+4)(x+6)]+16\)
\(=(x^2+10x+16)(x^2+10x+24)+16\)
\(=a(a+8)+16\) (Đặt \(x^2+10x+16=a\) )
\(=a^2+2.4.a+4^2=(a+4)^2\)
\(=(x^2+10x+16+4)^2\)
\(=(x^2+10x+20)^2\)
b) \((x^2+x)(x^2+x+1)-6\)
\(=(x^2+x)^2+(x^2+x)-6\)
\(=(x^2+x)^2-2(x^2+x)+3(x^2+x)-6\)
\(=(x^2+x)(x^2+x-2)+3(x^2+x-2)\)
\(=(x^2+x-2)(x^2+x+3)\)
\(=(x^2-x+2x-2)(x^2+x+3)\)
\(=[x(x-1)+2(x-1)](x^2+x+3)\)
\(=(x-1)(x+2)(x^2+x+3)\)
c)
\((x^2-4x)^2-8(x^2-4x)+15\)
\(=(x^2-4x)^2-3(x^2-4x)-5(x^2-4x)+15\)
\(=(x^2-4x)(x^2-4x-3)-5(x^2-4x-3)\)
\(=(x^2-4x-3)(x^2-4x-5)\)
\(=(x^2-4x-3)(x^2+x-5x-5)\)
\(=(x^2-4x-3)[x(x+1)-5(x+1)]=(x^2-4x-3)(x+1)(x-5)\)