Tìm x : X : 1/4 + X x 3 + x : 0,5 + x = 2024
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a, 2\(^3\) . x + 2005\(^0\) . x = 994-15:3+1\(^{2025}\)
8 .x + 1 . x = 990
x . [ 8 +1 ] = 990
x . 9 = 990
x = 990 : 9
x = 110
a: \(\left(2^3\right)^{1^{2005}}\cdot x+2005^0\cdot x=9915:3+1^{2025}\)
=>\(8\cdot x+1\cdot x=3305+1\)
=>\(9x=3306\)
=>\(x=\dfrac{3306}{9}=\dfrac{1102}{3}\)
b: \(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
=>\(2^x+2^x\cdot2+2^x\cdot4+2^x\cdot8=480\)
=>\(2^x\left(1+2+4+8\right)=480\)
=>\(2^x\cdot15=480\)
=>\(2^x=32\)
=>\(2^x=2^5\)
=>x+5
`@` `\text {Ans}`
`\downarrow`
`1.`
`13 \times 2525 - 25 \times 1313`
`= 13 \times 101 \times 25 - 25 \times 13 \times 101`
`= 13 \times 25 \times ( 101 - 101)`
`= 13 \times 25 \times 0`
`= 0`
`2.`
`(4 \times x - 2) \times (2024 - x) = x`
`4x(2024 - x) - 2(2024 - x) - x = 0`
`4x \times 2024 - 4x \times x - [ 2 \times 2024 + 2 \times (-x) ] = 0`
`8096 - 4x \times x - (4048 - 2x) = 0`
`8096 - 4x \times x - 4048 + 2x = 0`
`4048 - x(4x + 2) = 0`
`x(4x + 2) = 4048`
Bạn xem lại đề ;-; mình nghĩ lp 5 chưa hc mấy dạng ntnay ;-;.
\(1\dfrac{1}{2}\times1\dfrac{1}{3}\times1\dfrac{1}{4}\times...\times1\dfrac{1}{2023}\times1\dfrac{1}{2024}\)
\(=\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{4}\right)\times...\times\left(1+\dfrac{1}{2023}\right)\times\left(1+\dfrac{1}{2024}\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\dfrac{6}{5}\times...\times\dfrac{2024}{2023}\times\dfrac{2025}{2024}\)
\(=\dfrac{3\times4\times5\times...\times2024\times2025}{2\times3\times4\times...\times2023\times2024}\)
\(=\dfrac{2025}{2}\)
\(=1012,5\)
\(\left|2x-1\right|+\left(\dfrac{2}{3}-x\right)^{2024}=0\)
\(\left|2x-1\right|=-\left(\dfrac{2}{3}-x\right)^{2024}\)
Vì \(VT\ge0;VP\le0\)
Dấu "=" xảy ra <=> \(\left\{{}\begin{matrix}2x-1=0\\\dfrac{2}{3}-x=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{2}{3}\end{matrix}\right.\)(Loại)
a, 7\(x\).(2\(x\) + 10) =0
\(\left[{}\begin{matrix}x=0\\2x+10=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=0\\2x=-10\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
Vậy \(x\in\) {-5; 0}
b, -9\(x\) : (2\(x\) - 10) = 0
9\(x\) = 0
\(x\) = 0
c, (4 - \(x\)).(\(x\) + 3) = 0
\(\left[{}\begin{matrix}4-x=0\\x+3=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
Vậy \(x\in\) {-3; 4}
Lời giải:
$x:\frac{1}{4}+x\times 3+x:0,5+x=2024$
$x\times 4+x\times 3+x\times 2+x=2024$
$x\times (4+3+2+1)=2024$
$x\times 10=2024$
$x=2024:10=202,4$