4 | + | 4 | + … + | 4 | = | |
6 x 8 | 8 x 10 | 126 x 128 |
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a) x^2 - 2xy + y^2 - z^2
b) x^8 + x^4 + 1
c) x^4 + 4^2
d) 4x^4 + 81
e) x(x + 4)(x + 6)(x + 10) + 128
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a: \(=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
b: \(=x^8+2x^4+1-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\)
\(=\left(x^4+2x^2+1-x^2\right)\left(x^4-x^2+1\right)\)
\(=\left(x^2+1+x\right)\left(x^2+1-x\right)\left(x^4-x^2+1\right)\)
d: \(=4x^4+81+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
e: \(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)
\(=\left(x^2+10x\right)^2+24\left(x^2+10x\right)+128\)
\(=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)
\(=\left(x^2+10x+8\right)\left(x+2\right)\left(x+8\right)\)
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\(\Leftrightarrow\frac{\left(x+a\right)\left(3a^2x^2+a^2+8ax+x^2+3\right)\left(3a^6x^6+27a^6x^4+33a^6x2+a^6+72a^5x^5+24a^5x^3+72a^{5x}+27a^4x^6+459a^4x^4+441a^4x^2+33a^4+240a^3x^5+800a^3x^3+240a^3x+33a^2x^6+441a^2x^4+459x^2a^2+27a^2+75ax^5+240ax^3+72ax+x^6+33x^4+27x^2+3\right)}{\left(a^2+3\right)\left(a^6+33a^4+27a^{2+3}\right)\left(x^{2+3}\right)\left(x^6+33x^4+27x^2+3\right)}=0\)
mấy nhân tử sau ko cần chú ý đâu :)) chỉ cần chú ý đến x+a=0 <=>x=-a thôi :))
bài này đúng 100% nhé chỉ sợ gõ sai thôi, ko tin có thể dùng máy tính kiểm tra
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d) \(F=\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)(1)
Đặt \(x^2+x+1=t\)
\(\Rightarrow\left(1\right)=t\left(t+1\right)-12=t^2+t-12\)
\(=t^2+4t-3t-12\)
\(=t\left(t+4\right)-3\left(t+4\right)=\left(t-3\right)\left(t+4\right)\)(2)
Mà \(x^2+x+1=t\)(ẩn phụ)
Nên \(\left(2\right)=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
c) \(E=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)(1)
Đặt \(x^2+7x+10=t\)
\(\Rightarrow\left(1\right)=t\left(t+2\right)-24=t^2+2t-24\)
\(=t^2+6t-4t-24\)
\(=t\left(t+6\right)-4\left(t+6\right)=\left(t-4\right)\left(t+6\right)\)(2)
Mà \(x^2+7x+10=t\)(ẩn phụ)
Nên \(\left(2\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
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a: =>3(x+4)=115
=>x+4=115/3
hay x=103/3
b: =>\(8^3\cdot\left(12x-64\right)=4\cdot8^4\)
\(\Leftrightarrow12x-64=32\)
=>12x=96
hay x=8
c: \(\Leftrightarrow\left(4x+28\right)\cdot23+55=175\)
=>(4x+28)x23=120
=>4x+28=120/23
=>4x=-524/23
hay x=-131/23
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`(3xx4xx7)/(5xx3xx4)=7/5`
`(2xx5xx6xx8)/(6xx2xx8xx9)=5/9`
`(4xx5xx6)/(3xx10xx8)= (4xx5xx6)/(3xx5xx2xx4xx2)= 6/(3xx2xx2)= 6/(6xx2)=1/2`
\(a,\dfrac{3\times4\times7}{5\times3\times4}=\dfrac{7}{5}\)
\(b,\dfrac{2\times5\times6\times8}{6\times2\times8\times9}=\dfrac{5}{9}\)
\(c,\dfrac{4\times5\times6}{3\times10\times8}=\dfrac{2}{4}=\dfrac{1}{2}\)
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1/ 10(X-7)-8(X+5)=6(-5)+24
10x - 70 - 8x - 40 = -30 +24
2x - 110 = -6
2x = 104
x=52
2/ 8(X-|-7|)-6(X-2)=|-8|.6-50
8(x - 7) - 6(x-2) = 8.6 - 50
8x - 56 - 6x +12 =48 -50
2x - 44 = -2
2x = 42
x=21
3/ 2(4X-8)-7(3+X)=|-4|(3-2)
8x-16 - 21 - 7x = 4.1
x-37=4
x=41
4/ 12(X-4)=6(x-2)-16(X+3)=7|-4|
12x - 48 = 6x - 12 - 16x -48 =7.4
12x - 48 = 28
12x=76
x=19/3
5/ 4(X-5)-7(5-X)+10(5-X)=-3
4x - 20 -35 +7x + 50 -10x = -3
x - 5 = -3
x = -2
Chúc bạn học tốt!
A = \(\dfrac{4}{6\times8}\) + \(\dfrac{4}{8\times10}\) + ......+\(\dfrac{4}{126\times128}\)
A = 2x ( \(\dfrac{2}{6\times8}\) + \(\dfrac{2}{8\times10}\) +......+ \(\dfrac{2}{126\times128}\))
A = 2 x ( \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\) - \(\dfrac{1}{10}\) + .......+ \(\dfrac{1}{126}\) - \(\dfrac{1}{128}\))
A = 2 x ( \(\dfrac{1}{6}\) - \(\dfrac{1}{128}\))
A = 2 x \(\dfrac{61}{384}\)
A = \(\dfrac{61}{192}\)