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a) 2x+2x+3=144
2x . 1 + 2x . 23 = 144
2x . ( 1 + 23 ) = 144
2x . 9 = 144
2x = 144 : 9
2x = 16
2x = 24
=> x = 4
b) 72x + 72x+2 = 2450
72x . 1 + 72x . 72= 2450
72x . ( 1 + 72 ) = 2450
72x . 50 = 2450
72x = 2450 : 50
72x = 49
72x = 72
=> 2x = 2
=> x = 1
Ta có : 2x + 2x + 3 = 144
=> 2x (1 + 23) = 144
=> 2x . 9 = 144
=> 2x = 144 : 9
=> 2x = 16
=> 2x = 24
=> x = 4
a/ \(7^{2x}+7^{2x+2}=2450\)
\(\Leftrightarrow7^{2x}+2^{2x}.7^2=2450\)
\(\Leftrightarrow7^{2x}\left(1+49\right)=2450\)
\(\Leftrightarrow7^{2x}.50=2450\)
\(\Leftrightarrow7^{2x}=79\)
\(\Leftrightarrow7^{2x}=7^2\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=1\left(tm\right)\)
Vậy ....
b/ Ta có :
\(A=1+2+2^2+.......+2^{2016}\)
\(\Leftrightarrow2A=2+2^2+......+2^{2017}\)
\(\Leftrightarrow2A-A=\left(2+2^2+.......+2^{2017}\right)-\left(1+2+....+2^{2016}\right)\)
\(\Leftrightarrow A=2^{2017}-1\)
Mà \(B=2^{2017}-1\)
\(\Leftrightarrow A=B\)
Ta có : 72x + 72x + 2 = 2450
=> 72x(1 + 72) = 2450
=> 72x . 50 = 2450
=> 72x = 49
\(\Leftrightarrow\orbr{\begin{cases}7^{2x}=7^2\\7^{2x}=\left(-7\right)^2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=2\\2x=-2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
72x+72x+2=2450
=>72x(1+72)=2450
=>72x.50=2450
=>72x=2450/50
=>72x =49=72
=>2x=2
=>x=1
Vậy x=1
\(A=x^7-2x^4+3x^3-3x^4+2x^7-x+7-2x^3\)
\(A=3x^7-5x^4+x^3-x+7\)
\(B=3x^2-4x^4-3x^2-5x^5-0,5x-2x^2-3\)
\(B=-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-5x^4+x^3-x+7-5x^5-4x^4-2x^2-0,5x-3\)
\(A+B=3x^7-9x^4+x^3-1,5x+4\)
\(A-B=3x^7-5x^4+x^3-x+7+5x^5+4x^4+2x^2+0,5x+3\)
\(A-B=3x^7-x^4+x^3-0,5x+10+5x^5\)
7^2+7^2x+2=2401
=>7^2+7^2x.7^2=2401
=>7^2.(1+7^2x)=2401
=>1+7^2x+1=49=7^2
=>....