( 5/4x - 2/3 )^4 = 57/16 + 3/2
=> ( 5/4x - 2/3 )^4 = 81/16
=> ( 5/4x - 2/3 )^4 = 3^4/2^4
=> 5/4x - 2/3 = 3/2
=> 5/3x = 13/6
=> x = 13/10
Vậy x = 13/10
\(\left(\frac{5}{4}x-\frac{2}{3}\right)^4-\frac{3}{2}=\frac{57}{16}\)
\(\left(\frac{5}{4}x-\frac{2}{3}\right)^4-\frac{3}{2}=\frac{57}{16}+\frac{3}{2}\)
\(\left(\frac{5}{4}x-\frac{2}{3}\right)=\frac{81}{16}\)
Ta xét 2th:
Th1: \(\frac{5}{4}x-\frac{2}{3}=\left(\frac{81}{16}\right)^{\frac{1}{4}}\)
\(\Rightarrow x=\frac{26}{15}\)
Th2: \(\frac{5}{4}x-\frac{2}{3}=-\left(\frac{81}{16}\right)^{\frac{1}{4}}\)
\(\Rightarrow x=-\frac{2}{3}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{26}{15}\\x=-\frac{2}{3}\end{cases}}\)
