bài 1: tìm x
a) x-6/13 + x-6/14=x-6/15 + x-6/16
b) x+1 /65 +x+3/63= x+5/61+x+7/59
xong đầu đc ctrlhn
bài 1: tìm x
a) x-6/13 + x-6/14=x-6/15 + x-6/16
b) x+1 /65 +x+3/63= x+5/61+x+7/59
xong đầu đc ctrlhn
Đáp án:
b. x=-66
Giải thích các bước giải:
\(\begin{array}{l}
a.\dfrac{{x – 6}}{{13}} + \dfrac{{x – 6}}{{14}} = \dfrac{{x – 6}}{{15}} + \dfrac{{x – 6}}{{16}}\\
\to \dfrac{{x – 6}}{{13}} + \dfrac{{x – 6}}{{14}} – \dfrac{{x – 6}}{{15}} – \dfrac{{x – 6}}{{16}} = 0\\
\to \left( {x – 6} \right)\left( {\dfrac{1}{{13}} + \dfrac{1}{{14}} – \dfrac{1}{{15}} – \dfrac{1}{{16}}} \right) = 0\\
\to x – 6 = 0\\
\to x = 6\\
b.\dfrac{{x + 1}}{{65}} + \dfrac{{x + 3}}{{63}} = \dfrac{{x + 5}}{{61}} + \dfrac{{x + 7}}{{59}}\\
\to \dfrac{{x + 1}}{{65}} + 1 + \dfrac{{x + 3}}{{63}} + 1 = \dfrac{{x + 5}}{{61}} + 1 + \dfrac{{x + 7}}{{59}} + 1\\
\to \dfrac{{x + 66}}{{65}} + \dfrac{{x + 66}}{{63}} = \dfrac{{x + 66}}{{61}} + \dfrac{{x + 66}}{{59}}\\
\to \dfrac{{x + 66}}{{65}} + \dfrac{{x + 66}}{{63}} – \dfrac{{x + 66}}{{61}} – \dfrac{{x + 66}}{{59}} = 0\\
\to \left( {x + 66} \right)\left( {\dfrac{1}{{65}} + \dfrac{1}{{63}} – \dfrac{1}{{61}} – \dfrac{1}{{59}}} \right) = 0\\
\to x + 66 = 0\\
\to x = – 66
\end{array}\)