Question

1 Rút gọn:

(x+5)^3-x^3-125

2 Tìm x:

x^3+6x^3+12x+8=0

Answer 1

(x+5)³-x³-125

=x³+5³-x³-5³

=0

Answer 2

1. \(\left(x+5\right)^3-x^3-125\)

\(=x^3+15x^2+75x+125-x^3-125\)

\(=15x^2+75x\)

2. \(x^3+6x^2+12x+8=0\)

\(\Leftrightarrow x^3+2x^2+4x^2+8x+4x+8=0\)

\(\Leftrightarrow x^2\left(x+2\right)+4x\left(x+2\right)+4\left(x+2\right)=0\)

\(\Leftrightarrow\left(x^2+4x+4\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)^2\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)^3=0\)

\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

Answer 3

1. \(\left(x+5\right)^3-x^3-125\)  

=\(x^3+3\cdot x^2\cdot5+3\cdot x\cdot5^2+5^3-x^3-125\)  

=\(x^3+15x^2+75x+125-x^3-125\)  

=\(15x^2+75x\)   

=\(15x\left(x+5\right)\)      

2. \(x^3+6x^2+12x+8=0\)   

\(x^3+2x^2+4x^2+8x+4x+8=0\)   

\(x^2\left(x+2\right)+4x\left(x+2\right)+4\left(x+2\right)=0\) 

\(\left(x+2\right)\left(x^2+4x+4\right)=0\) 

\(\left(x+2\right)\left(x+2\right)^2=0\) 

 \(\left(x+2\right)^3=0\)    

\(x+2=0\) 

\(x=-2\)

Answer 4

( x + 5 )³ - x³ - 125

= x³ + 15x² + 75x + 125 - x³ - 125

= 15x² + 75x = 15x( x + 5 )

x³ + 6x² + 12x + 8 = 0

<=> x³ + 3.x².2 + 3.x.2² + 2³ = 0

<=> ( x + 2 )³ = 0

<=> x + 2 = 0

<=> x = -2