Question

Answer 1

giup tui gaps

 

Answer 2

\(C=2+2^2+2^3+...+2^{100}\)

\(2C=2^2+2^3+2^4+...+2^{101}\)

\(2C-C=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)

\(C=2^{101}-2\)

để \(2^{2x-1}-2=C\)

⇒\(2^{2x-1}=2^{101}\)

⇒2x-1=101

⇒x=51

Answer 3

a: Ta có: \(\left(x-\dfrac{1}{3}\right)^2-\dfrac{1}{4}=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{1}{2}\\x-\dfrac{1}{3}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{6}\\x=-\dfrac{1}{6}\end{matrix}\right.\)