Đáp án:
$\\$
`(2x-15)^5 = (2x-15)^3`
`↔ (2x-15)^5 - (2x-15)^3 = 0`
`↔ (2x-15)^3 . (2x-15)^2 - (2x-15)^3 = 0`
`↔ [ (2x - 15)^2 - 1] (2x-15)^3 = 0`
Trường hợp 1 :
`↔ (2x-15)^2-1=0`
`↔ (2x-15)^2 =0 + 1`
`↔ (2x-15)^2 = 1`
`↔` \(\left[ \begin{array}{l}(2x-15)^2=1^2\\(2x-15)^2=(-1)^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x-15=1\\2x-15=-1\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=1+15\\2x=-1+15\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=16\\2x=14\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=16÷2\\x=14÷2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=8\\x=7\end{array} \right.\)
Trường hơp 2 :
`↔ (2x-15)^3 = 0`
`↔ 2x - 15 = 0`
`↔ 2x = 0 + 15`
`↔ 2x = 15`
`↔ x = 15 ÷ 2`
`↔ x = 15/2`
Vậy `x=8,x=7,x=15/2`
