Question

1 Tìm x biết :

a) \(\left(5x+1\right)^2\) = \(\dfrac{36}{49}\)

b) \(\left(x-\dfrac{2}{9}\right)^3\) = \(\left(\dfrac{2}{3}\right)^6\)

c) \(\left(8x-1\right)^{2n+1}\) = \(5^{2n+1}\) \(\left(n\in N\right)\)

Answer 1

a) \(\left(5x+1\right)^2=\dfrac{36}{49}\)

\(\left(5x+1\right)^2=\left(\pm\dfrac{6}{9}\right)\)\(^2\)

\(5x+1=\pm\dfrac{6}{9}\)

+) \(5x+1=\dfrac{6}{9}\)

\(5x=\dfrac{6}{9}-1=\dfrac{6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{9}\)

\(x=\dfrac{-5}{9}:5=\dfrac{-1}{45}\)

+) \(5x+1=\dfrac{-6}{9}\)

\(5x=\dfrac{-6}{9}-1=\dfrac{-6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{3}\)

\(x=\dfrac{-5}{3}:5=\dfrac{-5}{15}\)

vậy \(x\in\left\{\dfrac{-5}{15};\dfrac{-1}{45}\right\}\)