\(a.\left(x+1\right)\left(x^2-x+1\right)-x\left(x^2-5\right)=71\)

\(\Leftrightarrow x^3+1-x^3+5x=71\)

\(\Leftrightarrow5x=71-1\)

\(\Leftrightarrow5x=70\)

\(\Leftrightarrow x=70:5=14\)

\(b.\left(2x-3\right)^3-8x\left(x-1\right)^2+4x\left(4x+1\right)+27=0\)

\(\Leftrightarrow8x^3-12x^2+18x-27-8x\left(x^2-2x+1\right)+16x^2+4x+27=0\)

\(\Leftrightarrow8x^3-12x^2+18x-27-8x^3+16x^2-8x+16x^2+4x+27=0\)

\(\Leftrightarrow20x^2+14x=0\)

\(\Leftrightarrow x\left(20x+14\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\20x+14=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\frac{7}{10}\end{cases}}}\)

a) ta có: (x+1)(x^2 -x+1) -x(x^2 -5)=71

          <=>x^3 +1 -x^3 +5x=71

         <=>5x=70

         <=>x=14

b) ta có:(2x-3)^3 -8x(x-1)^2 +4x(4x+1)+27=0

        <=>[ (2x-3)^3  +27)]  -  [ 8x(x-1)^2  -4x(4x+1)]=0

       <=> (2x-3+3)[ (2x-3)^2 - (2x-3).3  +3^2]   - 2x [ 4(x^2 -2x +1) -2(4x+1)]=0

       <=>2x( 4.x^2 - 12x +9 - 6x +9 +9)   -  2x( 4.x^2 -8x+4 -8x -2)=0

       <=>2x(4.x^2  -18x +27)  -  2x(4.x^2 -16x +2)=0

      <=>2x(4.x^2 -18x+27 -4.x^2 +16x-2)=0

     <=>2x(25-2x)=0

<=>x=0 hoặc 25-2x=0 <=> x=0 hoặc x=25/2

c: =117-89-223-71+105+111+223

=6-160

=-154

a)(9x+2)x3=60

        9x+2 =60:3

        9x+2  =20

              9x =20-2

              9x=18

                x=18:9

                 x=2

a,x=2

b,x=2

c,x=9

o phan a 

(9x+2)*3=60

9x+2=20

9x=18

x=2

o phan b

71+(26-3x)/5=75

(26-3x)/5=75-71=4

26-3x=4*5=20

3x=26-20=6

x=6/3=2

vay x=2

o phan c 

(x-6)^2=9

(x-6)^2=3^2

=>x-6=3

=>x=9

vay x =9

ở phần d 

1+3+.....+x=465

=>(x+1)*(x-1)/2+(x+1)=465

=>(x+1)*(x-1)/2

1) Do x ∈ Z và 0 < x < 3

⇒ x ∈ {1; 2}

2) Do x ∈ Z và 0 < x ≤ 3

⇒ x ∈ {1; 2; 3}

3) Do x ∈ Z và -1 < x ≤ 4

⇒ x ∈ {0; 1; 2; 3; 4}

=>6x + 1 + 2 + 3 + 4 + 5 + 6 + = 71

=>6x + 21 = 71

6x = 71 - 21 = 50

=>x = 50/6 = 25/3

(x+1)+(x+2)+(x+3)+(x+4)+(x+6)=71

=x*5+1+2+3+4+5+6=71

=x*5+21=71

=x*5=71-21

=x*5=50

=x=50:5

x=10

vậy x=10

a: \(\dfrac{x+5}{x-1}+\dfrac{8}{x^2-4x+3}=\dfrac{x+1}{x-3}\)

=>(x+5)(x-3)+8=x^2-1

=>x^2+2x-15+8=x^2-1

=>2x-7=-1

=>x=3(loại)

b: \(\dfrac{x-4}{x-1}-\dfrac{x^2+3}{1-x^2}+\dfrac{5}{x+1}=0\)

=>(x-4)(x+1)+x^2+3+5(x-1)=0

=>x^2-3x-4+x^2+3+5x-5=0

=>2x^2+2x-6=0

=>x^2+x-3=0

=>\(x=\dfrac{-1\pm\sqrt{13}}{2}\)

e: =>x^2-2x+1+2x+2=5x+5

=>x^2+3=5x+5

=>x^2-5x-2=0

=>\(x=\dfrac{5\pm\sqrt{33}}{2}\)

g: (x-3)(x+4)*x=0

=>x=0 hoặc x-3=0 hoặc x+4=0

=>x=0;x=3;x=-4