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15 tháng 10 2017

\(a,\left(x+1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=17\)\(\Leftrightarrow x^3+3x^2+3x+1+8-x^3+3x^2+6x-17=0\)\(\Leftrightarrow6x^2+9x-8=0\)

\(\Leftrightarrow x^2+\dfrac{3}{2}x-\dfrac{4}{3}=0\)

\(\Leftrightarrow\left(x^2+\dfrac{3}{2}x+\dfrac{9}{16}\right)-\dfrac{9}{16}-\dfrac{4}{3}=0\)

\(\Leftrightarrow\left(x+\dfrac{3}{4}\right)^2=\dfrac{91}{48}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{3}{4}=\sqrt{\dfrac{91}{48}}\\x+\dfrac{3}{4}=-\sqrt{\dfrac{91}{48}}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{91}{48}}-\dfrac{3}{4}\\x=-\sqrt{\dfrac{91}{48}}-\dfrac{3}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-9+\sqrt{273}}{12}\\x=-\dfrac{9+\sqrt{273}}{12}\end{matrix}\right.\)

b, \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)

\(\Leftrightarrow x^3+8-x^3+2x-15=0\)

\(\Leftrightarrow2x=7\Rightarrow x=\dfrac{7}{2}\)

21 tháng 7 2016

a,\(\Leftrightarrow\left(x-1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)-17=0\)

\(\Leftrightarrow x^3-3x^2+3x-1+8-x^3+3x^2+6x-17=0\)

\(\Leftrightarrow9x-10=0\)

\(\Leftrightarrow x=\frac{10}{9}\)

 

21 tháng 7 2016

b,\(\Leftrightarrow x^3+8-x^3+2x-15=0\)

\(\Leftrightarrow2x=7\)

\(\Leftrightarrow x=\frac{7}{2}\)

16 tháng 6 2018

a.\(\Leftrightarrow\left(x-1\right)^3+8-x^3+3x\left(x+2\right)=17\)

    \(\Leftrightarrow x^3-3x^2+3x-1+8-x^3+3x^2+6x=17\)

   \(\Leftrightarrow9x+7=17\)

   \(\Leftrightarrow9x=10\Leftrightarrow x=\frac{10}{9}\)

24 tháng 7 2019

a) (x - 1)3 + (2 - x)(4 + 2x + x2) + 3x(x + 2) = 12

<=> x3 - 2x2 + x - x2 + 2x - 1 + 8 + 4x + 2x2 - 4x - 2x2 + 3x2 + 6x = 17

<=> 9x + 7 = 17

<=> 9x = 17 - 7

<=> 9x = 10

<=> x = \(\frac{10}{9}\)

b) (x + 2)(x2 - 2x + 4) - x(x2 - 2) = 15

<=> x3 - 2x2 + 4x + 2x2 - 4x + 8 - x3 + 2x = 15

<=> 2x + 8 = 15

<=> 2x = 15 - 8

<=> 2x = 7

<=> x = \(\frac{7}{2}\)

c) (x - 3)3 - (x - 3)(x2 + 3x + 9) + 9(x2 + 1)2 = 15

<=> x3 + 45x - 18 - x3 - 3x2 - 9x + 3x2 + 9x + 27 = 15

<=> 45x + 9 = 15

<=> 45x = 15 - 9

<=> 45x = 6

<=> x = \(\frac{6}{45}\)

d) x(x - 5)(x + 5) - (x + 2)(x2 - 2x + 4) = 3

<=> x3 - 25x - x3 + 2x2 - 4x - 8 = 3

<=> -25x - 8 = 3

<=> -25x = 3 + 8

<=> -25x = 11

<=> x = \(-\frac{11}{25}\)

24 tháng 7 2019

a)\(\left(x-1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=17\)

\(=>x^3-3x^2+3x-1+8-x^3+3x^2+6x=17\)

\(=>9x+7=17=>9x=10=>x=\frac{10}{9}\)

a: Ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)

\(\Leftrightarrow x^3+8-x^3-2x=15\)

\(\Leftrightarrow2x=-7\)

hay \(x=-\dfrac{7}{2}\)

b: Ta có: \(\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6\left(x+1\right)^2=49\)

\(\Leftrightarrow-6x^2+12x+56+6x^2+12x+6=49\)

\(\Leftrightarrow24x=-13\)

hay \(x=-\dfrac{13}{24}\)

5 tháng 10 2020

a) \(\left(x+3\right)^2-\left(x-4\right)\left(x+8\right)=1\)

\(\Leftrightarrow\left(x^2+6x+9\right)-\left(x^2+4x-32\right)-1=0\)

\(\Leftrightarrow2x=-40\)

\(\Rightarrow x=-20\)

b) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=15\)

\(\Leftrightarrow x^3+27-x^3+4x=15\)

\(\Leftrightarrow4x=-12\)

\(\Rightarrow x=-3\)

c) \(\left(x-2\right)^2-\left(x+3\right)^2-4\left(x+1\right)=5\)

\(\Leftrightarrow\left(x^2-4x+4\right)-\left(x^2+6x+9\right)-\left(4x+4\right)=5\)

\(\Leftrightarrow-14x=14\)

\(\Rightarrow x=-1\)

5 tháng 10 2020

d) \(\left(2x-3\right)\left(2x+3\right)-\left(x-1\right)^2-3x\left(x-5\right)=-44\)

\(\Leftrightarrow4x^2-9-\left(x^2-2x+1\right)-\left(3x^2-15x\right)=-44\)

\(\Leftrightarrow17x=-34\)

\(\Rightarrow x=-2\)

e) \(\left(x-2\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=49\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+27+6x^2+12x+6=49\)

\(\Leftrightarrow24x=24\)

\(\Rightarrow x=1\)

17 tháng 10 2023

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13 tháng 10 2021

Bn gửi từng câu sẽ có nhều ng trl hơn nhé

tý mk giải câu a cho cần ko

24 tháng 8 2020

a) (x - 1)3 + (2 - x)(4 + 2x + x2) + 3x(x + 2) = 16

x3 - 3x2 + 3x - 1 + 8 - x3 + 3x2 + 6x - 16 = 0

9x - 9 = 0

9x = 9

x = 1

Vậy x ∈ {1}

b) ( x + 2)(x2 - 2x + 4) - x(x2 - 2) = 16

x3 + 8 - x3 + 2x - 16 = 0

2x - 8 = 0

2x = 8

x = 4

Vậy x ∈ {4}

c) x(x - 5)(x + 5) - (x + 2)(x2 - 2x + 4) = 17

x3 - 25x - x3 - 8 - 17 = 0

-25x - 25 = 0

-25x = 25

x = -1

Vậy x ∈ {1}

d) (x - 3)3 - (x - 3)(x2 + 3x + 9) + 9(x + 1)2 = 15

x3 - 9x2 + 27x - 27 - x3 + 27 + 9x2 + 18x + 9 - 15 = 0

45x - 6 = 0

45x = 6

x = \(\frac{2}{15}\)

Vậy x ∈ {\(\frac{2}{15}\)}

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