2x+2x+2=80. Tìm x
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80-(5+80)=3-(x-7)
80-85=3-(x-7)
-5=3-(x-7)
3+(-5)=x-7
-2=x-7
7+(-2)=x
5=x
a/ \(80-\left(5+80\right)=3-\left(x-7\right)\)
\(\Leftrightarrow3-\left(x-7\right)=80-85=-5\)
\(\Leftrightarrow x-7=3-\left(-5\right)=8\)
\(\Rightarrow x=8+7=15\)
b/ \(150-\left(2x+1\right)=150-29=121\)
\(\Leftrightarrow2x+1=150-121=29\)
\(\Leftrightarrow2x=29-1=28\)
\(\Rightarrow x=28:2=14\)
d. Áp dụng BĐT Caushy Schwartz ta có:
\(x+y+\dfrac{1}{x}+\dfrac{1}{y}\le x+y+\dfrac{\left(1+1\right)^2}{x+y}=x+y+\dfrac{4}{x+y}\le1+\dfrac{4}{1}=5\)
-Dấu bằng xảy ra \(\Leftrightarrow x=y=\dfrac{1}{2}\)
a/
$(2x-3\frac{1}{2})+250\text{%}=6,2$
$(2x-\frac{7}{2})+2,5=6,2$
$2x-\frac{7}{2}=6,2-2,5=3,7$
$2x=3,7+\frac{7}{2}=7,2$
$x=7,2:2=3,6$
b/
$(25\text{%}-4\frac{1}{2}x)-2\frac{1}{2}.4^2=5,25$
$(0,25-\frac{9}{2}x)-40=5,25$
$0,25-\frac{9}{2}x=45,25$
$\frac{9}{2}x=0,25-45,25=-45$
$x=-45:\frac{9}{2}=-10$
\(\Rightarrow\left(2x-1\right)^{100}-\left(2x-1\right)^{80}=0\)
Đặt 2x - 1 = t ta có :
\(t^{100}-t^{80}=0\Rightarrow t^{80}\left(t^{20}-1\right)=0\)
=> \(t^{80}=0\) hoặc \(t^{20}-1=0\)
=> t = 0 hoặc \(t^{20}=1=\left(-1\right)^2\)
=> t= 0 hoặc t = 1 hoặc t = -1
(+) t = 0 => 2x - 1 = 0 => x = 1/2
(+) t = 1 => 2x - 1 = 1 => x = 1
(+) t= - 1 => 2x - 1 = -1 => x = 0
tick đúng nha
=> (2x -1)100 - (2x -1)80 = 0
=> (2x -1)80. [(2x-1)20 - 1] = 0
=> (2x -1)80 = 0 hoặc (2x -1)20 = 1
+) (2x -1)80 = 0 => 2x - 1 = 0 => x = 1/2
+) (2x -1)20 = 1 => 2x - 1 = 1 hoặc 2x - 1 = -1
=> 2x = 2 hoặc 2x = 0 => x = 1 hoặc x = 0
Vậy....
a) \(3^{x+2}\cdot5^{y-3}=45^x\)
\(\Rightarrow3^{x+2}\cdot5^{y-3}=\left(3^2\right)^x\cdot5^x\)
\(\Rightarrow3^{x+2}\cdot5^{y-3}=3^{2x}\cdot5^x\)
\(\Rightarrow\left\{{}\begin{matrix}3^{x+2}=3^{2x}\\5^{y-3}=5^x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+2=2x\\y-3=x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\y-3=2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\y=5\end{matrix}\right.\)
2^x+2^x+2=80
2^x(1+2^2)=80
2^x.5=80
2^x=16
2^x=2^4=>x=4