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Tìm x, y biết :
\(\left|x+3\right|+\left|x-1\right|=\dfrac{16}{\left|y-2\right|+\left|y+2\right|}\)
Ta có: \(\left|x+3\right|+\left|x-1\right|=\left|x+3\right|+\left|1-x\right|\ge\left|x+3+1-x\right|=4\)
\(\left|y-2\right|+\left|y+2\right|=\left|2-y\right|+\left|y+2\right|\ge\left|2-y+y+2\right|=4\)
\(\Rightarrow\dfrac{16}{\left|y-2\right|+\left|y+2\right|}\le\dfrac{16}{4}=4\Rightarrow\left|x+3\right|+\left|x-1\right|\ge\dfrac{6}{\left|y-2\right|+\left|y+2\right|}\)
Dấu '=' xảy ra <=> (x+3)(1-x)\(\ge0\) và (2-y)(y+2)\(\ge0\)
Vì x,y \(\in Z\Rightarrow\left\{{}\begin{matrix}x\in\left\{-3;-2;-2;0;1\right\}\\y\in\left\{-2;-1;0;1;2\right\}\end{matrix}\right.\)
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tìm x biết:
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)
\(4x+\frac{15}{16}=\frac{23}{16}\)
\(4x=\frac{1}{2}\)
\(x=\frac{1}{8}\)
Vậy \(x=\frac{1}{8}\)
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\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)
\(\Rightarrow\left(x+x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=\frac{23}{16}\)
\(\Rightarrow5x+\frac{15}{32}=\frac{23}{16}\)
\(\Rightarrow5x=\frac{23}{16}-\frac{15}{32}\)
\(\Rightarrow5x=\frac{31}{32}\)
\(\Rightarrow x=\frac{31}{32}.\frac{1}{5}=\frac{31}{160}\)
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Xem thêm câu trả lời
text{Tìm x, biết:}a) left(19x+2.5^2right):14left(13-8right)^2-4^2b) x+left(x+1right)+left(x+2right)+...+left(x+30right)1240c) 11-left(-53+xright)97d) -left(x+84right)+213-16
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\(\text{Tìm x, biết:}\)
\(a\)) \(\left(19x+2.5^2\right):14=\left(13-8\right)^2-4^2\)
\(b\)) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=1240\)
\(c\)) \(11-\left(-53+x\right)=97\)
\(d\)) \(-\left(x+84\right)+213=-16\)
Tìm số nguyên x biết \(\left(x^2-\frac{4}{25}\right)\left(x^2-4\right)\left(x^2-\frac{16}{9}\right)\left(x^2-10\right)< 10\)
tìm x biết:
\(\left(x-4\right)\left(x^2+4x+16\right)-x\left(x^2-6\right)=2\)
Tìm x biết:
\(\sqrt{\sqrt{\sqrt{\left(x-4\right)^8}.\sqrt{\left(x+16\right)^{16}}}}=0\)
Tìm x biết: \(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
tìm x biết:
a, \(\left(x+4\right)^2-\left(x+1\right)\left(x-1\right)=16\)
b, \(\left(2x-1\right)^2-\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\)
a,\((x+4)^2-(x+1)(x-1)=16\)
\(\Rightarrow x^2+8x+16-x^2+1=16\)
\(\Rightarrow 8x=-1\Rightarrow x=-\dfrac{1}{8}\)
b,\((2x-1)^2-(x+3)^2-5(x+7)(x-7)=0\)
\(\Rightarrow 4x^2-4x+1-(x^2+6x+9)-5(x^2-49)=0\)
\(\Rightarrow 4x^2-4x+1-x^2-6x-9-5x^2-245=0\)
\(\Rightarrow -x^2-10x-244=0\)
\(\Rightarrow -(x^2-10x+25)-219=0\)
\(\Rightarrow -(x-5)^2-219=0\)
\(\Rightarrow (x-5)^2+219=0\)
Mà \((x-5)^2+219>0\) suy ra PT vô nghiệm
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\(\dfrac{\left(-2\right)^x}{16}=-8\)
tìm x biết
\(\dfrac{\left(-2\right)^x}{16}=-8\\ \Leftrightarrow\left(-2\right)^x=-8.16=\left(-2\right)^3.\left(-2\right)^4=\left(-2\right)^{3+4}=\left(-2\right)^7\\ Vậy:x=7\)
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Tìm x biết: \(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
=>4x+(1/2+1/4+1/8+1/16)=1
<=>4x+15/16=1
=>4x=1/16
=>x=1/16:4=1/64
vậy x=1/64
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\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Rightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)
\(\Rightarrow4x+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right)=1\)
\(\Rightarrow4x+\left(1-\frac{1}{16}\right)=1\)
\(\Rightarrow4x+\frac{15}{16}=1\)
\(\Rightarrow4x=1-\frac{15}{16}\)
\(\Rightarrow x=\frac{1}{16}:4\)
\(\Rightarrow x=\frac{1}{64}\)
vậy \(x=\frac{1}{64}\)
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