Toán Lớp 8: 1. Giải phương trình sau
a, $\frac{x+1}{65}$ + $\frac{x+3}{63}$ = $\frac{x+5}{61}$ + $\frac{x+7}{59}$
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Toán Lớp 8: 1. Giải phương trình sau
a, $\frac{x+1}{65}$ + $\frac{x+3}{63}$ = $\frac{x+5}{61}$ + $\frac{x+7}{59}$
Comments ( 2 )
$\begin{array}{l}
\dfrac{{x + 1}}{{65}} + \dfrac{{x + 3}}{{63}} = \dfrac{{x + 5}}{{61}} + \dfrac{{x + 7}}{{59}}\\
\Rightarrow \dfrac{{x + 1}}{{65}} + 1 + \dfrac{{x + 3}}{{63}} + 1 = \dfrac{{x + 5}}{{61}} + 1 + \dfrac{{x + 7}}{{59}} + 1\\
\Rightarrow \dfrac{{x + 66}}{{65}} + \dfrac{{x + 66}}{{63}} = \dfrac{{x + 66}}{{61}} + \dfrac{{x + 66}}{{59}}\\
\Rightarrow \left( {x + 66} \right)\left( {\dfrac{1}{{65}} + \dfrac{1}{{63}} – \dfrac{1}{{61}} – \dfrac{1}{{59}}} \right) = 0\\
\dfrac{1}{{65}} < \dfrac{1}{{61}},\dfrac{1}{{63}} < \dfrac{1}{{59}} \Rightarrow \dfrac{1}{{65}} + \dfrac{1}{{63}} – \dfrac{1}{{61}} – \dfrac{1}{{59}} < 0\\
\Rightarrow x + 66 = 0\\
\Rightarrow x = – 66
\end{array}$
Vậy $x=-66$ thỏa mãn yêu cầu đề bài.
Giải đáp:
Lời giải và giải thích chi tiết:
$\ \dfrac{x + 1}{65} + \dfrac{x + 3}{63} = \dfrac{x + 5}{61} + \dfrac{x + 7}{59} $
$\ ⇒ \dfrac{x + 1}{65} + 1 + \dfrac{x + 3}{63} + 1 = \dfrac{x + 5}{61} + 1 + \dfrac{x + 7}{59} + 1 $
$\ ⇒ \dfrac{x + 1 + 65}{65} + \dfrac{x + 3 + 63}{63} = \dfrac{x + 5 + 61}{61} + \dfrac{x + 7 + 59}{59} $
$\ ⇒ \dfrac{x + 66}{65} + \dfrac{x + 66}{63} – \dfrac{x + 66}{61} – \dfrac{x + 66}{59} = 0 $
$\ ⇒ (x + 66)(\dfrac{1}{65} + \dfrac{1}{63} – \dfrac{1}{61} – \dfrac{1}{59}) = 0 $
Mà $\ \dfrac{1}{65} + \dfrac{1}{63} – \dfrac{1}{61} – \dfrac{1}{59} \neq 0 ∀ x $
$\ ⇒ x + 66 = 0 $
$\ ⇔ x = – 66 $