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a) => 4/3x = 7/9 - 4/9 = 1/3
=> x = 1/3 : 4/3 = 1/4
b) => 5/2 - x = 9/14 : (-4/7) = -9/8
=> x = 5/2 - (-9/8) = 5/2 + 9/8 = 29/8
c) => 3x = 2 và 2/3 - 3/4 = 8/3 - 3/4 = 23/12
=> x = 23/12 : 3 = 23/36
D) => -5/6 - x = 1/4
=> x = -5/6 - 1/4 = -13/12
a) \(\dfrac{4}{9}+\dfrac{4}{3}x=\dfrac{7}{9}\)
\(\dfrac{4}{3}x=\dfrac{7}{9}-\dfrac{4}{9}=\dfrac{1}{3}\)
\(x=\dfrac{1}{3}:\dfrac{4}{3}\)
\(x=\dfrac{1}{4}\)
b) \(\left(\dfrac{5}{2}-x\right)\left(-\dfrac{4}{7}\right)=\dfrac{9}{14}\)
\(\dfrac{5}{2}-x=\dfrac{9}{14}:\left(-\dfrac{4}{7}\right)=-\dfrac{9}{8}\)
\(x=\dfrac{5}{2}-\left(-\dfrac{9}{8}\right)\)
\(x=\dfrac{29}{8}\)
c) \(3x+\dfrac{3}{4}=2\dfrac{2}{3}\)
\(3x+\dfrac{3}{4}=\dfrac{8}{3}\)
\(3x=\dfrac{8}{3}-\dfrac{3}{4}=\dfrac{23}{12}\)
\(x=\dfrac{23}{12}:3\)
\(x=\dfrac{23}{36}\)
d) \(-\dfrac{5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)
\(-\dfrac{5}{6}-x=\dfrac{1}{4}\)
\(x=-\dfrac{5}{6}-\dfrac{1}{4}\)
\(x=-\dfrac{13}{12}\)
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x=(-2-sqrt(164))/-10=(1+sqrt(41))/5=1.481
x=(-2+sqrt(164))/-10=(1-sqrt(41))/5=-1.081
kích cho minh nha
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\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=2021\)
\(\left(x+x+x+...+x\right)+\left(1+2+...+99\right)=2021\)
\(100x+\left(1+2+...+99\right)=2021\)
Ta tính tổng \(A=1+2+...+99\) (Số số hạng của tổng là 99)
\(A=\left(1+99\right)+\left(2+98\right)+...+\left(49+51\right)+50\)
\(A=100+100+...+100+50=100\times49+50=4950\)
Vậy \(100x+4950=2021\)
Suy ra \(100x=2021-4950=-2929\), hay \(x=-29,29\)
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\(\left(a^2+3b^2\right)\left(1+3\right)\ge\left(a+3b\right)^2\)
\(\Rightarrow\sqrt{a^2+3b^2}\ge\sqrt{\dfrac{\left(a+3b\right)^2}{4}}=\dfrac{a+3b}{2}\)
Tương tự:
\(\sqrt{b^2+3c^2}\ge\dfrac{b+3c}{2}\) ; \(\sqrt{c^2+3a^2}\ge\dfrac{c+3a}{2}\)
Cộng vế \(\Rightarrow VT\ge\dfrac{4\left(a+b+c\right)}{2}=6\)
Dấu "=" xảy ra khi \(a=b=c=1\)
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`Answer:`
a. \(\left(x-3\right)+\left(x-2\right)+\left(x-1\right)+...+9+10+11=11\)
\(\Leftrightarrow x-3+x-2+x-1+...+9+10+11=11\)
\(\Leftrightarrow3x+\left(-3-2-1+0+...+11\right)=11\)
\(\Leftrightarrow3x+60=11\)
\(\Leftrightarrow3x=-49\)
\(\Leftrightarrow x=-\frac{49}{3}\)
b. \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Leftrightarrow100x+[\left(100+1\right).100:2]=5750\)
\(\Leftrightarrow100x+5050=5750\)
\(\Leftrightarrow100x=700\)
\(\Leftrightarrow x=7\)
c. \(2^x+2^{x+1}+2^{x+2}=960-2^{x+3}\)
\(\Leftrightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=960\)
\(\Leftrightarrow2^x+2.2^x+4.2^x+8.2^x=960\)
\(\Leftrightarrow2^x.\left(1+2+4+8\right)=960\)
\(\Leftrightarrow2^x.15=960\)
\(\Leftrightarrow2^x=64\)
\(\Leftrightarrow x=6\)