Question

[Nguyen Thi Thanh Thao]

+Tim x : 

a ) \(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)  

b )\(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\)

c ) \(\left(x+1\right)^{x+2}=\left(x-1\right)^{x+6}\) (x ϵ Z )

d ) \(\left(2x+3\right)^{2016}=\left(2x+3\right)^{2018}\)

e ) \(\frac{3}{x+2.x+5}+\frac{5}{x+5.x+10}+\frac{7}{x+10.x+17}=\frac{x}{x+2.x+17}\) Với  \(x\notin\left\{-2;-5;-10;-17\right\}\)

Answer 1

[Ngô Tấn Đạt]

\(a\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\\ =>\left(x-\frac{1}{2}\right)=\frac{1}{3}\\ =>x=\frac{1}{3}+\frac{1}{2}\\ =>x=\frac{5}{6}\)

b) \(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\\ =>\left(x+\frac{1}{2}\right)=\frac{2}{5}\\ =>x=\frac{-1}{10}\)

d) (2x+3)²⁰¹⁶=(2x+3)²⁰¹⁸ khi 2x+3=0 hoặc 1 

Nếu 2x+3=0 

=2x=-3 ( loại ) 

Nếu 2x+3=1

=>2x=-2

=>x=-1 ( thỏa )