Question

Tìm x 

a, (2x - 15) ⁵  = ( 2x - 15) ³

b, x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 2013) = 2035147

Answer 1

b, x + (x + 1) + (x + 2) + ..... + (x + 2013) = 2035147 

x + (x + x + .... + x) + (1 + 2 + .... + 2013) = 2035147 

x + 2013x + 2027091 = 2035147 

2014x = 2035147 - 2027091 = 8056

=> x = 8056 : 2014 = 4 

Answer 2

a) ( 2x - 15 )⁵ = ( 2x - 15 )³

( 2x - 15 )⁵ - ( 2x - 15 )³ = 0

\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}2x-15=0\\\left(2x-15\right)^2=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=15\\2x-15=1\text{ hoặc }2x-15=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{15}{2}\\x=8\text{ hoặc }x=7\end{cases}}}\)

b, x + ( x + 1 ) + ( x + 2 ) + ... + ( x + 2013) = 2035147

( x + x + x + ... + x ) + ( 1 + 2 + ... + 2013 ) = 2035147

2014x + 2027091 = 2035147

2014x = 2035147 - 2027091

2014x = 8056

x = 8056 : 2014

x = 4