10,07 - [3,927 - (3,63 - \(\dfrac{2}{20}\)) ] < (hoặc bằng) x < (hoặc bằng) 1,5 . (9,2 - \(\dfrac{2}{5}\)) + (3,2 - 3,12) . (4\(\dfrac{1}{10}\) - 2,85)
a, -150(1352-41) / (1352-41)(150-15) <x< (2400:48)-250 / 350 - (3600:12)
b, 10,07 - [ 3,927 - ( 3,63 - 3/20) ] < hoặc bằng x < hoặc bằng 1,5. (9,2-2/5) + (3,2-3,12) (41/10 -2,85 )
Đề là gì vậy bạn, x còn thêm điều kiện gì không như x ∈ Z,...v.v.
Tìm số nguyên x biết:
a)\(\frac{-150\left(1352-41\right)}{\left(1352-41\right)\left(50-45\right)}\)<x<\(\frac{\left(2400:48\right)-250}{350-\left(3600:12\right)}\)
b)10,07-[3,927-(3,63-\(\frac{3}{20}\))\(\le\)x\(\le\)1,5 \(\left(9,2-\frac{2}{5}\right)\)+(3,2-3,12).(\(4\frac{1}{10}\)-2,25)
tìm X
\(10.07-\left[3,927-\left(3,63-\frac{3}{20}\right)\right]\le x\le1,5.\left(9,2-\frac{2}{5}\right)+\left(3,2-3,12\right).\left(4\frac{1}{10}-2,35\right)\)
\(\left(x\in Z\right)\)
\(\text{VT = }10,07-3,927+3,63-\frac{3}{20}=9,623\)
\(VP=13,8-\frac{3}{5}+\frac{7}{50}=13,34\)
\(\text{Vì }x\in Z\Rightarrow x\left\{10;11;12;13\right\}\)
Chọn câu trả lời đúng \(\left(2x+\dfrac{1}{5}\right)\left(-\dfrac{3}{5}x+\dfrac{4}{7}\right)=0\) thì:
A. x = \(\dfrac{-1}{10}\) hoặc x = \(\dfrac{20}{21}\)
B. x = \(\dfrac{20}{21}\)
C. x = \(-\dfrac{1}{10}\)
D. x = \(-\dfrac{20}{21}\)
Giải BPT giùm mình với các bạn , thực sự mình cần rất gấp ạ !
1) \(\dfrac{2x+1}{2}+3>=\dfrac{3-5x}{3}-\dfrac{4x-1}{4}\)
2) \(\dfrac{5x-3}{5}+\dfrac{2x+1}{4}< =\dfrac{2-3x}{2}-5\)
*Chú thích : < = là bé hơn hoặc bằng
> = là lớn hơn hoặc bằng.
Tìm x, y biết
\((\dfrac{1}{2}.x-3)^10+(y^2-\dfrac{1}{81})^20\) lớn hơn hoặc bằng 0
Bài 59:Thay tỉ số giữa các số hữu tỉ bằng tỉ số giữa các số nguyên:
a)2,04:(-3,12);
b)(\(-1\dfrac{1}{2}\)):1,25;
c)4:\(5\dfrac{3}{4}\);
d)\(10\dfrac{3}{7}\):\(5\dfrac{3}{14}\).
a) \(2.04:\left(-3.12\right)=\dfrac{204}{-312}=\dfrac{-17}{26}\)
b) \(\left(-1\dfrac{1}{2}\right):1.25=\dfrac{-3}{2}:\dfrac{5}{4}=\dfrac{-3}{2}\cdot\dfrac{4}{5}=\dfrac{-12}{10}=\dfrac{-6}{5}\)
c) \(4:5\dfrac{3}{4}=4:\dfrac{23}{4}=4\cdot\dfrac{4}{23}=\dfrac{16}{23}\)
d) \(10\dfrac{3}{7}:5\dfrac{3}{14}=\dfrac{73}{7}:\dfrac{73}{14}=\dfrac{2}{1}\)
1.Cmr , với mọi số tự nhiên n lớn hơn hoặc bằng 1
a) \(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+....+\dfrac{1}{\left(2n\right)^2}< \dfrac{1}{2}\)
b) \(\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+....+\dfrac{1}{\left(2n+1\right)^2}< \dfrac{1}{4}\)
2.Cmr với mọi số tự nhiên lớn hơn hoặc bằng 2
\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+...+\dfrac{1}{n^2}< \dfrac{2}{3}\)
a) Đặt \(A=\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{\left(2n\right)^2}\)
\(A=\dfrac{1}{2^2}\left(1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}\right)\)
Ta có:
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{\left(n-1\right)n}\)
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n-1}-\dfrac{1}{n}\)
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}< 1-\dfrac{1}{n}\)
\(\Rightarrow1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}< 1-\dfrac{1}{n}+1\)
\(\Rightarrow1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}< 2-\dfrac{1}{n}\)
\(\Rightarrow\dfrac{1}{2^2}\left(1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}\right)< \dfrac{1}{2^2}\left(2-\dfrac{1}{2}\right)\)
\(\Rightarrow A< \dfrac{1}{2^2}.2-\dfrac{1}{2^2}.\dfrac{1}{2}\)
\(\Rightarrow A< \dfrac{1}{2}-\dfrac{1}{2^3}< \dfrac{1}{2}\)
Vậy \(A< \dfrac{1}{2}\left(Đpcm\right)\)
b) Đặt \(B=\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{\left(2n+1\right)^2}\)
Ta có:
\(B< \dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\)
\(B< \dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{\left(2n-1\right)\left(2n+1\right)}\right)\)
\(B< \dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\right)\)
\(B< \dfrac{1}{2}\left(1-\dfrac{1}{2n+1}\right)\)
\(B< \dfrac{1}{2}\left(\dfrac{2n+1}{2n+1}-\dfrac{1}{2n+1}\right)\)
\(B< \dfrac{1}{2}.\dfrac{2n}{2n+1}\)
\(B< \dfrac{2n}{4n+2}\)
\(B< \dfrac{2n}{2\left(2n+1\right)}\)
\(B< \dfrac{n}{2n+1}\)
M= \(\dfrac{3}{2}\sqrt{32x}-\dfrac{1}{3}\sqrt{18x}+\dfrac{2}{5}\sqrt{50x}-4\sqrt{2x}\) (x lớn hơn hoặc bằng 0)
giải chi tiết giúp mk vớiiiii ạ
\(M=\dfrac{3}{2}\cdot4\sqrt{2x}-\dfrac{1}{3}\cdot3\sqrt{2x}+\dfrac{2}{5}\cdot5\sqrt{2x}-4\sqrt{2x}=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)