CMR nếu: (a+b+c-d)(a-b-c-d) = (a+b-c+d)(a-b+c+d) thì a+b/a-b = c-d/c+d

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1. Đáp án:

   $\text{(a + b + c – d)(a – b – c – d) = ( a + b – c + d)(a – b + c + d)}$

   $\text{⇒ $\dfrac{a+b}{a-b}$ = $\dfrac{c-d}{c+d}$}$

   Giải thích các bước giải:

   $\text{Giải:}$

   $\text{Ta có : }$

   $\text{(a + b + c – d)(a – b – c – d) = ( a + b – c + d)(a – b + c + d)}$

   $\text{⇒ $\dfrac{a + b + c – d}{a + b – c + d}$ = $\dfrac{a – b + c + d}{a – b – c – d}$ ⇔ $\dfrac{(a+b) + (c-d)}{(a-b) – (c+d)}$ = $\dfrac{(a+b) + (c+d)}{(a-b) – (c+d)}$}$

   $\text{Đặt A = a + b ; B = c – d ; C = a – b ; D = c + d. Ta được:}$

   $\text{$\dfrac{A + B}{A – B}$ = $\dfrac{C + D }{C – D}$ ⇒ $\dfrac{A}{B}$ = $\dfrac{C}{D}$ ⇔ $\dfrac{a + b}{c-d}$ = $\dfrac{a-b}{c+d}$ }$

   $\text{⇒ $\dfrac{a+b}{a-b}$ = $\dfrac{c-d}{c+d}$}$

   $\text{Ta được :}$

   $\text{(a + b + c – d)(a – b – c – d) = ( a + b – c + d)(a – b + c + d)}$

   $\text{⇒ $\dfrac{a+b}{a-b}$ = $\dfrac{c-d}{c+d}$}$

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