$(2{x}$ – $15)^{5}$ = $(2{x}$ – $15)^{3}$ Các bạn trình bày rõ ràng giùm mình nhé

Đáp án:

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`(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`