19837630 : 3755 x 65
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35 x 34 + 35 x 65 + 65 x 75 + 65 x 45
= ( 35 x 34 + 35 x 65 ) + ( 65 x 75 + 65 x 45 )
= 35 x ( 34 + 65 ) + 65 x ( 75 + 45 )
= 35 x 99 + 65 x 120
= 3465 + 7800
= 11265
\(\dfrac{x+1}{65}+\dfrac{x+3}{63}\) = \(\dfrac{x+5}{61}\) + \(\dfrac{x+7}{59}\)
<=> \(\dfrac{x+1}{65}+1+\dfrac{x+3}{63}+1\) = \(\dfrac{x+5}{61}\) + 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
3,527 + 65 x 73 + 65 x 27 + 3,573
= 3,527 + 65 x ( 73 + 27 ) + 3,573
= 3,527 + 65 x 100 + 3,573
= 3,527 + 6500 + 3,573
= 6507,1
20,10x35-19,45x65+20,10x65-19,45x35
=(35+65)x20,10+(35+65)x19,45
=100x20,10-100x19,45
=100x(20,10-19,45)
=100x0,65=65
Đặt \(\hept{\begin{cases}\sqrt[3]{65+x}=a\\\sqrt[3]{65-x}=b\end{cases}}\)
\(\Rightarrow a^2+4b^2=5ab\)
\(\Leftrightarrow\left(b-a\right)\left(4b-a\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}a=b\\a=4b\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}\sqrt[3]{65+x}=\sqrt[3]{65-x}\\\sqrt[3]{65+x}=4\sqrt[3]{65-x}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}65+x=65-x\\65+x=4\left(65-x\right)\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=39\end{cases}}\)