(x+5)³-x³-125

=x³+5³-x³-5³

=0

1. \(\left(x+5\right)^3-x^3-125\)

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

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

2. \(x^3+6x^2+12x+8=0\)

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

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

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

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

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

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

\(\frac{5}{6}x+\frac{1}{2}-\frac{1}{3}x=0,75x-\frac{7}{8}\)  

\(\frac{5}{6}x-\frac{1}{3}x-0,75x=-\frac{7}{8}-\frac{1}{2}\) 

\(\frac{5}{6}x-\frac{1}{3}x-\frac{3}{4}x=-\frac{11}{8}\) 

\(\frac{1}{2}x-\frac{3}{4}x=-\frac{11}{8}\)  

\(-\frac{1}{4}x=-\frac{11}{8}\)  

\(x=-\frac{11}{8}:-\frac{1}{4}\)  

\(x=\frac{11}{2}\)  

Có:    \(\frac{x}{2}=\frac{y}{3}\)

=>   \(\frac{4x}{8}=\frac{3y}{9}=\frac{4x-3y}{8-9}=\frac{-2}{-1}=2\)

=>   \(\hept{\begin{cases}4x=16\\3y=18\end{cases}}\)

=>   \(\hept{\begin{cases}x=4\\y=6\end{cases}}\)

\(\frac{x}{2}=\frac{y}{3}\Leftrightarrow\frac{4x}{8}=\frac{3y}{9}\) và \(4x-3y=-2\)

Áp dụng tính chất dãy tỉ số bằng nhau, ta có : \(\frac{4x}{8}=\frac{3y}{9}=\frac{4x-3y}{8-9}=\frac{-2}{-1}=2\)

\(\Leftrightarrow4x=8.2=16\Leftrightarrow16\div4=4\)

\(\Leftrightarrow3y=2.9=18\Leftrightarrow y=18\div3=6\)

Vậy \(x=4;y=6\)

= \(3^2x22-3^3x19=3^2x22-3^2x3x19=3^2x\left(22-19x3\right)=9x\left(-35\right)=\left(-315\right)\)

học tốt nhé!

\(4\cdot5^2-\frac{81}{3^2}\) 

=\(4\cdot25-\frac{81}{9}\) 

= 100 - 9 

= 91 

2^2×5^2-9^2:3^2

=(2×5-9:3)^2

=7^2

x-2\(\frac{1}{4}\)=3\(\frac{1}{2}\)

x-\(\frac{9}{4}\)=\(\frac{7}{2}\)

x           =    \(\frac{7}{2}\)+\(\frac{9}{4}\)

x            = \(\frac{23}{4}\)

các câu còn lại, bạn tự làm nhé

X - 2 1/4 = 3 1/2                    X + 2 3/4 = 5 2/3                    3 1/2 : X = 1 3/5                    X : 1 1/2 = 2 2/5                       

X -    9/4 =  7/2                      X +  11/4 = 17/3                        7/2 : X =   8/5                     X :    3/2  =   12/5

X            = 7/2 + 9/4              X             = 17/3 - 11/4                      X = 7/2 : 8/5               X             =  12/5 x 3/2

X            =     13/4                 X             =    35/12                           X = 35/16                   X             =   18/5

Nhớ tíck cho mik nha

Sai chỗ nào thì bảo mik 

a) \(a^2+b^2+c^2=ab+bc+ac\)

\(\Leftrightarrow2\left(a^2+b^2+c^2\right)=2\left(ab+bc+ac\right)\)

\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2bc-2ac=0\)

\(\Leftrightarrow\left(a-b\right)^2+\left(c-a\right)^2+\left(b-c\right)^2=0\)

Ta có : \(\hept{\begin{cases}\left(a-b\right)^2\ge0\\\left(c-a\right)^2\ge0\\\left(b-c\right)^2\ge0\end{cases}}\)

\(\Rightarrow\left(a-b\right)^2+\left(c-a\right)^2+\left(b-c\right)^2=0\)

\(\Leftrightarrow a=b=c\)

a. \(a^2+b^2+c^2=ab+bc+ca\)

\(\Leftrightarrow2a^2+2b^2+2c^2=2ab+2bc+2ca\)

\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2ab-2ca=0\)

\(\Leftrightarrow\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ca+a^2\right)=0\)

\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}a-b=0\\b-c=0\\c-a=0\end{cases}}\Leftrightarrow a=b=c\left(đpcm\right)\)

5x² - 5xy + 4y - 4x

= 5x ( x - y ) - 4 ( x - y )

= ( 5x - 4 ) ( x - y )

( x + y )³ + ( x - y )³

= 2x³ + 6xy²

= 2x ( x² + 3y² )

5 x^2 - 5xy + 4y - 4x 

= 5x ( x - y ) - 4 ( x - y ) 

= ( x - y ) ( 5x - 4 ) 

( x + y )^3 + ( x - y )^3 

= \(x^3+3x^2y+3xy^2+y^3+x^3-3x^2y+3xy^2-y^3\) 

= \(2x^3+6xy^2\) 

=\(2x\left(x^2+3y^2\right)\) 

kết quả bằng -1.05169894

a) \(\left(2x+1\right)^3=27\)

\(\Leftrightarrow2x+1=3\)

\(\Leftrightarrow x=1\)

b) \(\left(2x-1\right)^3=125\)

\(\Leftrightarrow2x-1=5\)

\(\Leftrightarrow x=3\)

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

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow x=1\)

d) \(\left(2x-1\right)^5=x^5\)

\(\Leftrightarrow2x-1=x\)

\(\Leftrightarrow x=1\)

a. ( 2x + 1 )³ = 27

<=> ( 2x + 1 )³ = 3³

<=> 2x + 1 = 3

<=> 2x = 2

<=> x = 1

b. ( 2x - 1 )³ = 125

<=> ( 2x - 1 )³ = 5³

<=> 2x - 1 = 5

<=> 2x = 6

<=> x = 3

c. ( x + 1 )⁴ = 2x⁴

<=> x + 1 = 2x

<=> x = 1

d. ( 2x - 1 )⁵ = x⁵

<=> 2x - 1 = x

<=> x = 1