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P(x) + Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x) + ( 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4)
= x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x + 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4
= ( x^5 - x^5 ) - ( 2x^2 + 4x^2) + ( 7x^4 + 5x^4) - ( 9x^3 - 2x^3) - 1/4x - 1/4
= 6x^2 + 12x^4 - 6x^3 - 1/4x - 1/4
P(x) - Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 -1/4x) - ( 5x^4 - x^5 + 4x^2 - 2x^3 -1/4)
= x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x - 5x^4 + x^5 - 4x^2 + 2x^3 + 1/4
= ( x^5 + x^5) - ( 2x^2 - 4x^2) + ( 7x^4 - 5x^4) - ( 9x^3 + 2x^3) - 1/4x + 1/4
= 2x^5 - (-2)x^2 + 2x^4 - 11x^3 - 1/4x + 1/4
P(x)=x^5+ 7x^4- 9x^3+ 2x^2-1/4x-0
Q(x)=(-x^5+5x^4- 2x^3+ 4x^2+0x-1/4
= 12x^4-11x^3+ 6x^2-1/4x-1/4
a)
\(512-\left(128-5x\right)=3x+12\\ 512-128+5x=3x+12\\ 384+5x=3x+12\\ 5x-3x=12-384\\ 2x=-372\\ x=\left(-372\right):2\\ x=-186\)
b)
\(\left(2x-1\right)+\left(4x-2\right)+...+\left(400x-200\right)=5+10+...+1000\\ \left(2x+4x+...+400x\right)-\left(1+2+...+200\right)=5+10+...+1000\\ x\left(2+4+...+400\right)=\left(5+10+...+1000\right)+\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=5\cdot\left(1+2+...+200\right)+1\cdot\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=\left(5+1\right)\cdot\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=6\cdot\left(1+2+...+200\right)\\ \Rightarrow2x=6\\ x=6:2\\ x=3\)
c)
\(\left(x+2\right)+\left(4x+4\right)+\left(7x+6\right)+...+\left(25x+18\right)+\left(28x+20\right)=1560\\ \left(x+4x+7x+...+25x+28x\right)+\left(2+4+6+...+18+20\right)=1560\\ x\left(1+4+7+...+25+28\right)+110=1560\\ 145x+110=1560\\ 145x=1560-110\\ 145x=1450\\ x=1450:145\\ x=10\)
d)
\(x+4x+5x+9x+14x+...+97x=500\\ x\left(1+4+5+9+14+...+97\right)=500\)
Dãy số trong ngoặc có quy luật: Số thứ \(n\) bằng số thứ \(n-1\) cộng số thứ \(n-2\)
Suy ra dãy số đó là: \(1+4+5+9+14+23+37+60+97=250\)
Thế vào ta được:
\(250x=500\\ x=500:250\\ x=2\)
e)
\(720-\left[41-\left(2x-5\right)\right]=2^3\cdot5\\ 720-41+\left(2x-5\right)=8\cdot5\\ 720-41+2x-5=40\\ \left(720-41-5\right)+2x=40\\ 674+2x=40\\ 2x=40-674\\ 2x=-634\\ x=\left(-634\right):2\\ x=-317\)
f)
\(697:\dfrac{15x+364}{x}=17\\ \dfrac{15x+364}{x}=697:17\\ \dfrac{15x+364}{x}=41\\ \dfrac{15x+364}{x}\cdot x=41x\\ 15x+364=41x\\ 364=41x-15x\\ 364=26x\\ x=364:26\\ x=14\)
a) 7x - 5 = 16 b) 156 - 2x = 82 c) 10x + 65 = 125
=> 7x = 16 + 5 => 2x = 156 - 82 => 10x = 125 - 65
=> 7x = 21 => 2x = 74 => 10x = 60
=> x = 21 : 7 => x = 74 : 2 => x = 60 : 10
=> x = 3 => x = 37 => x = 6
Vậy x = 3 Vậy x = 37 Vậy x = 6
d) 8x + 2x = 25.2 e) 15 + 5x = 40 f) 5x + 2x = 6 - 5
=> 10x = 50 => 5x = 40 - 15 => 7x = 1
=> x = 50 : 10 => 5x = 25 => x = 1 : 7
=> x = 5 => x = 25 : 5 => x = 1/7
Vậy x = 5 => x = 5 Vậy x = 1/7
Vậy x = 5
g) 5x + x = 150 : 2 + 3 h) 6x + 3x = 5 : 5 + 3 i) 5x + 3x = 3 : 3 . 4 + 12
=> 6x = 75 + 3 => 9x = 1 + 3 => 8x = 1 . 4 + 12
=> 6x = 78 => 9x = 4 => 8x = 4 + 12
=> x = 78 : 6 => x = 4 : 9 => 8x = 16
=> x = 13 => x = 4/9 => x = 16 : 8
Vậy x = 13 Vậy x = 4/9 => x = 2
Vậy x = 2
j) 4x + 2x = 68 - 2 : 2 k) 5x + x = 39 - 3 : 3 l) 7x - x = 5 : 5 + 3 . 2 - 7
=> 6x = 68 - 1 => 6x = 39 - 1 => 6x = 1 + 6 - 7
=> 6x = 67 => 6x = 38 => 6x = 7 - 7
=> x = 67 : 6 => x = 38 : 6 => 6x = 0
=> x = 67/6 => x = 19/3 => x = 0
Vậy x = 67/6 Vậy x = 19/3 Vậy x = 0
m) 7x - 2x = 6 : 6 + 44 : 11
=> 5x = 1 + 4
=> 5x = 5
=> x = 5 : 5
=> x = 1
Vậy x = 1
Mỏi tay ~~~~~~~~~~~~~~
a: Ta có: \(7x+25=144\)
\(\Leftrightarrow7x=119\)
hay x=17
b: Ta có: \(33-12x=9\)
\(\Leftrightarrow12x=24\)
hay x=2
c: Ta có: \(128-3\left(x+4\right)=23\)
\(\Leftrightarrow3\left(x+4\right)=105\)
\(\Leftrightarrow x+4=35\)
hay x=31
d: Ta có: \(71+\left(726-3x\right)\cdot5=2246\)
\(\Leftrightarrow5\left(726-3x\right)=2175\)
\(\Leftrightarrow726-3x=435\)
\(\Leftrightarrow3x=291\)
hay x=97
e: Ta có: \(720:\left[41-\left(2x+5\right)\right]=40\)
\(\Leftrightarrow41-\left(2x+5\right)=18\)
\(\Leftrightarrow2x+5=23\)
\(\Leftrightarrow2x=18\)
hay x=9
P(x) = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x
=x5+7x4-9x3-2x2-1/4x
Q(x) = 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4
=-x5+5x4-2x3+4x2-1/4
P(x)+Q(x)=x5+7x4-9x3-2x2-1/4x -x5+5x4-2x3+4x2-1/4
=x5-x5+7x4+5x4-9x3-2x3-2x2+4x2-1/4x-1/4
=12x4-11x3+2x2-1/4x-1/4
P(x)-Q(x)=x5+7x4-9x3-2x2-1/4x +x5-5x4+2x3-4x2+1/4
=x5+x5+7x4-5x4-9x3+2x3-2x2-4x2-1/4x-1/4
=2x5+2x4-7x3-6x2-1/4x-1/4