Question

tìm x

(3x-5)^8 = 1/125 ( 5-3x)^11

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gúp mk nha T^T

Answer 1

\(\left(3x-5\right)^8=\frac{1}{125}\left(5-3x\right)^{11}\)

\(\Leftrightarrow-\left(3x-5\right)^8=-\frac{1}{125}\left(3x-5\right)^{11}\)

\(\Leftrightarrow-1=-\frac{1}{125}\left(3x-5\right)^3\)

\(\Leftrightarrow\frac{1}{125}\left(3x+5\right)^3=1\)

\(\Leftrightarrow\left(3x-5\right)^3=125\)

\(\Leftrightarrow3x-5=\sqrt[3]{125}\)

\(\Leftrightarrow3x-5=5\)

\(\Leftrightarrow3x=10\)

\(\Leftrightarrow x=\frac{10}{3}\)

Vậy phương trình đã cho có tập nghiệm  \(S=\left\{\frac{10}{3}\right\}\)