(18x38+16x76-1)=(36x19+64x20-65)x X
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a,
( 18.38 + 16.76 - 1 ) = ( 39 x 19 + 64 x 20 - 65 )x
=> ( 684 + 1216 - 1) = ( 741 + 1280 - 65 )x
=> 1899 = 1956x
=> 1956x = 1899
=> x = 1899/1956
=> x = 633/652
Tương tự tiếp...
\(\dfrac{x+1}{65}+\dfrac{x+3}{63}\) = \(\dfrac{x+5}{61}\) + \(\dfrac{x+7}{59}\)
<=> \(\dfrac{x+1}{65}+1+\dfrac{x+3}{63}+1\) = \(\dfrac{x+5}{61}\) + 1 + \(\dfrac{x+7}{59}\) + 1
<=> \(\dfrac{x+66}{65}+\dfrac{x+66}{63}\) = \(\dfrac{x+66}{61}\) + \(\dfrac{x+66}{59}\)
<=> \(\dfrac{x+66}{65}+\dfrac{x+66}{63}\) - \(\dfrac{x+66}{61}\) - \(\dfrac{x+66}{59}\) = 0
<=> (x + 66) . (\(\dfrac{1}{65}+\dfrac{1}{63}+\dfrac{1}{61}+\dfrac{1}{59}\)) = 0
<=> x + 66 = 0
<=> x = -66
a.
Đặt \(\left\{{}\begin{matrix}\sqrt[3]{x+2}=a\\\sqrt[3]{x-2}=b\end{matrix}\right.\) ta được:
\(2a^2-b^2=ab\)
\(\Leftrightarrow\left(a-b\right)\left(2a+b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=b\\2a=-b\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}a^3=b^3\\8a^3=-b^3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=x-2\left(vô-nghiệm\right)\\8\left(x+2\right)=-\left(x-2\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-\dfrac{14}{9}\)
b.
Đặt \(\left\{{}\begin{matrix}\sqrt[3]{65+x}=a\\\sqrt[3]{65-x}=b\end{matrix}\right.\)
\(\Rightarrow a^2+4b^2=5ab\)
\(\Leftrightarrow\left(a-b\right)\left(a-4b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=b\\a=4b\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a^3=b^3\\a^3=64b^3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}65+x=65-x\\65+x=64\left(65-x\right)\end{matrix}\right.\)
\(\Leftrightarrow...\)
( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) = 65
( x + x + x + x + x ) + ( 1 + 2 + 3 + 4 = 5 ) = 65
x * 5 +15 = 65
x * 5 = 65 - 15
x * 5 = 50
x = 50 : 5
x = 10
( X + 1 ) + ( X + 2 ) + ( X + 3 ) + ( X + 4 ) + ( X + 5 ) = 65
X x 5 + ( 1 + 2 + 3 + 4 + 5 ) = 65
X x 5 + 15 = 65
X x 5 = 65 - 15
X x 5 = 50
X = 50 : 5
X = 10
18 x 38 + 16 x 38 x 2 -1 = (18 x 2 x 19 + 32 x 2 x 20 - 32 x 2 - 1) x X
X = (18 x 38 + 32 x 38 - 1) : (18 x 38 + 32 x 38 - 1)
X = 1