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20 tháng 12 2020
1, \(45+x^3-5x^2-9x=9\left(5-x\right)+x^2\left(x-5\right)\)
\(=\left(9-x^2\right)\left(x-5\right)=\left(3-x\right)\left(x+3\right)\left(x-5\right)\)
3, \(x^4-5x^2+4\)
Đặt \(x^2=t\left(t\ge0\right)\)ta có :
\(t^2-5t+4=t^2-t-4t+4=t\left(t-1\right)-4\left(t-1\right)\)
\(=\left(t-4\right)\left(t-1\right)=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
YN
29 tháng 3 2022
`Answer:`
1. `45+x^3-5x^2-9x`
`=x^3+3x^2-8x^2-24x+15x+45x`
`=x^2 .(x+3)-8x.(x+3)+15.(x+3)`
`=(x+3).(x^2-8x+15)`
`=(x+3).(x^2-5x-3x+15)`
`=(x-3).(x-5).(x-3)`
2. `x^4-2x^3-2x^2-2x-3`
`=x^4+x^3-3x^3+x^2+x-3x-3`
`=x^3 .(x+1)-3x^2 .(x+1)+x.(x+1)-3.(x+1)`
`=(x+1).(x^3-3x^2+x-3)`
`=(x+1).[x^3 .(x-3).(x-3)]`
`=(x+1).(x-3).(x^2+1)`
3. `x^4-5x^2+4`
`=x^4-x^2-4x^2+4`
`=x^2 .(x^2-1)-4.(x^2-1)`
`=(x^2-1).(x^2-4)`
`=(x-1).(x+1).(x-2).(x+2)`
4. `x^4+64`
`=x^4+16x^2+64-16x^2`
`=(x^2+8)^2-16x^2`
`=(x^2+8-4x).(x^2+8+4x)`
5. `x^5+x^4+1`
`=x^5+x^4+x^3-x^3+1`
`=x^3 .(x^2+x+1)-(x^3-1)`
`=x^3 .(x^2+x+1)-(x-1).(x^2+x+1)`
`=(x^2+x+1).(x^3-x+1)`
6. `(x^2+2x).(x^2+2x+4)+3`
`=(x^2+2x)^2+4.(x^2+2x)+3`
`=(x^2+2x)^2+x^2+2x+3.(x^2+2x)+3`
`=(x^2+2x+1).(x^2+2x)+3.(x^2+2x+1)`
`=(x^2+2x+1).(x^2+2x+3)`
`=(x+1)^2 .(x^2+2x+3)`
7. `(x^3+4x+8)^2+3x.(x^2+4x+8)+2x^2`
`=x^6+8x^4+16x^3+16x^2+64x+64+3x^3+12x^2+24x+2x^2`
`=x^6+8x^4+19x^3+30x^2+88x+64`
8. `x^3 .(x^2-7)^2-36x`
`=x[x^2.(x^2-7)^2-36]`
`=x[(x^3-7x)^2-6^2]`
`=x.(x^3-7x-6).(x^3-7x+6)`
`=x.(x^3-6x-x-6).(x^3-x-6x+6)`
`=x.[x.(x^2-1)-6.(x+1)].[x.(x^2-1)-6.(x-1)]`
`=x.(x+1).[x.(x-1)-6].(x-1).[x.(x+1)-6]`
`=x.(x+1).(x-1).(x^2-3x+2x-6).(x^2+3x-2x-6)`
`=x.(x+1).(x-1).[x.(x-3)+2.(x-3)].[x.(x+3)-2.(x+3)]`
`=x.(x+1)(x-1).(x-2).(x+2).(x-3).(x+3)`
9. `x^5+x+1`
`=x^5-x^2+x^2+x+1`
`=x^2 .(x^3-1)+(x^2+x+1)`
`=x^2 .(x-1).(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1).(x^3-x^2+1)`
10. `x^8+x^4+1`
`=[(x^4)^2+2x^4+1]-x^4`
`=(x^4+1)^2-(x^2)^2`
`=(x^4-x^2+1).(x^4+x^2+1)`
`=[(x^4+2x^2+1)-x^2].(x^4-x^2+1)`
`=[(x^2+1)^2-x^2].(x^4-x^2+1)`
`=(x^2-x+1).(x^2+x+1).(x^4-x^2+1)
11. ` x^5-x^4-x^3-x^2-x-2`
`=x^5-2x^4+x^4-2x^3+x^3-2x^2+x^2-2x+x-2`
`=x^4 .(x-2)+x^3 ,(x-2)+x^2 .(x-2)+x.(x-2)+(x-2)`
`=(x-2).(x^4+x^3+x^2+x+1)`
12. `x^9-x^7-x^6-x^5+x^4+x^3+x^2-1`
`=(x^9-x^7)-(x^6-x^4)-(x^5-x^3)+(x^2-1)`
`=x^7 .(x^2-1)-x^4 .(x^2-1)-x^3 .(x^2-1)+(x^2-1)`
`=(x^2-1).(x^7-x^4-x^3+1)`
`=(x-1)(x+1)(x^3-1)(x^4-1)`
`=(x-1)(x+1)(x^2+x+1)(x-1)(x^2-1)(x^2+1)`
`=(x-1)^2 .(x+1)(x^2+x+1)(x-1)(x+1)(x^2+1)`
`=(x-1)^3 .(x+1)^2 .(x^2+x+1)(x^2+1)`
13. `(x^2-x)^2-12(x^2-x)+24`
`=[ (x^2-x)^2-2.6(x^2-x)+6^2]-12`
`=(x^2-x+6)^2-12`
`=(x^2-x+6-\sqrt{12})(x^2-x+6+\sqrt{12})`
PT
18 tháng 9 2018
a) \(A=3\left(x+5\right)+x^2\)
Thay x = 1 vào A, ta được:
\(A=3\left(1+5\right)+1^2\)
\(A=3.6+1\)
\(A=19\)
b) \(B=3x\left(x+2\right)-x\left(x+1\right)\)
Thay x = -1 vào B, ta được:
\(B=3.\left(-1\right)\left(-1+2\right)-\left(-1\right)\left(-1+1\right)\)
\(B=-3-0\)
\(B=-3\)
c) \(C=7x\left(x-5\right)+3\left(x-2\right)\)
Thay x = 0 vào C, ta được:
\(C=7.0.\left(0-5\right)+3.\left(0-2\right)\)
\(C=0+3.\left(-2\right)\)
\(C=-6\)
d) \(D=-2x\left(x+1\right)+4\left(x+2\right)\)
Thay x = -1 vào D, ta được:
\(D=-2\left(-1\right)\left(-1+1\right)+4\left(-1+2\right)\)
\(D=0+4\)
\(D=4\)
e) \(E=x^2-x+2x\left(x+3\right)\)
Thay x = 2 vào E, ta được:
\(E=2^2-2+2.2\left(2+3\right)\)
\(E=4-2+4.5\)
\(E=22\)
f) \(F=5-4x\left(x-2\right)\)
Thay x = -1 vào F, ta được:
\(F=5-4.\left(-1\right)\left(-1-2\right)\)
\(F=5-12\)
\(F=-7\)
g) \(G=x\left(x-5\right)-2x\left(x+1\right)+x^2\)
Thay x = -2 vào G, ta được:
\(G=-2\left(-2-5\right)-2.\left(-2\right)\left(-2+1\right)+\left(-2\right)^2\)
\(G=14-4+4\)
\(G=14\)
h) \(H=x\left(7x+2\right)-5x\left(x+3\right)\)
Thay x = 1 vào H, ta được:
\(H=1\left(7.1+2\right)-5.1\left(1+3\right)\)
\(H=9-20\)
\(H=-11\)
i) \(I=3x^2-2x\left(x-5\right)+x\left(x-7\right)\)
Thay x = 10 vào I, ta được:
\(I=3.10^2-2.10\left(10-5\right)+10.\left(10-7\right)\)
\(I=300-100+30\)
\(I=230\)
16 tháng 3 2020
\(x\left(x-1\right)=x\left(x+3\right)\)
\(x^2-x=x^2+3x\)
\(x^2+x-x^2-3x=0\)
\(-2x=0\)
\(x=0\)
\(\left(x-1\right)\left(x+3\right)=x^2-4\)
\(x^2+3x-x-3=x^2-4\)
\(x^2+2x-3=x^2-4\)
\(x^2+2x-3-x^2+4=0\)
\(2x+1=0\)
\(2x=1\)
\(x=\frac{1}{2}\)
cj lm nốt nha , cj lm ms ý nghĩa , cố lên !
20 tháng 10 2018
1
a) \(\left(3x+1\right)\left(3x-1\right)=9x^2-1\)
\(\left(x+5y\right)\left(x-5y\right)=x^2-25y\)
b) \(\left(x-3\right)\left(x^2+3x+9\right)=x^3-27\)
\(\left(x-5\right)\left(x^2+5x+25\right)=x^3-125\)
26 tháng 10 2022
Bài 3:
a: \(\Leftrightarrow x^2+8x+16-x^2+1=16\)
=>8x+1=0
=>x=-1/8
b: \(\Leftrightarrow4x^2-4x+1+x^2+6x+9-5x^2+245=0\)
=>2x+255=0
=>x=-255/2
c: \(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6x^2+12x+6=49\)
=>24x+62=49
=>24x=-13
=>x=-13/24
d: =>x^3+8-x^3-2x=15
=>-2x=15-8=7
=>x=-7/2
DH
4 tháng 7 2017
a, \(-\left(x+3\right)\left(x-4\right)+\left(x+1\right)\left(x-1\right)=10\)
\(\Rightarrow-\left(x^2-4x+3x-12\right)+x^2-1=10\)
\(\Rightarrow-x^2+x+12+x^2-1=10\)
\(\Rightarrow x=10+1-12\Rightarrow x=-1\)
b, \(\left(2x-1\right)\left(x-2\right)-\left(x+3\right)\left(2x-7\right)=3\)
\(\Rightarrow2x^2-4x-x+2-\left(2x^2-7x+6x-21\right)=3\)
\(\Rightarrow2x^2-5x+2-2x^2+x+21=3\)
\(\Rightarrow-4x=3-21-2\Rightarrow-4x=-20\)
\(\Rightarrow x=5\)
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