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\(A=\frac{\left[\left(25-1\right):1+1\right]\left(25+1\right)}{2}=325.\)
\(B=\frac{\left[\left(51-3\right):2+1\right]\left(51+3\right)}{2}=675\)
\(C=\frac{\left[\left(81-1\right):4+1\right]\left(81+1\right)}{2}=861\)
a) \(3\left(x-5\right)+6=36\)
\(\Rightarrow3\cdot\left(x-5\right)=36-6\)
\(\Rightarrow3\cdot\left(x-5\right)=30\)
\(\Rightarrow x-5=10\)
\(\Rightarrow x=10+5\)
\(\Rightarrow x=15\)
b) \(200-8\cdot\left(x+7\right)=24\)
\(\Rightarrow8\cdot\left(x+7\right)=200-24\)
\(\Rightarrow8\cdot\left(x+7\right)=176\)
\(\Rightarrow x+7=\dfrac{176}{8}\)
\(\Rightarrow x+7=22\)
\(\Rightarrow x=22-7\)
\(\Rightarrow x=15\)
c) \(\left(x-890\right)\left(74-x\right)=0\)
+) \(x-890=0\)
\(\Rightarrow x=890\)
+) \(74-x=0\)
\(\Rightarrow x=74\)
d) \(\left(31-x\right)\cdot\left(x-64\right)=0\)
+) \(31-x=0\)
\(\Rightarrow x=31\)
+) \(x-64=0\)
\(\Rightarrow x=64\)
1014 : ( 124 - x ) = 13
124 - x = 1014 : 13
124 - x = 78
x = 124 - 78
x = 46
\(B=3^1+3^2+3^3+...+3^{100}\\3B=3^2+3^3+3^4+...+3^{101}\\3B-B=(3^2+3^3+3^4+...+3^{101})-(3^1+3^2+3^3+...+3^{100})\\2B=3^{101}-3\\\Rightarrow 2B+3=3^{101}\)
Mặt khác: \(2B+3=3^n\)
\(\Rightarrow 3^n=3^{101}\\\Rightarrow n=101(tm)\)
Vậy n = 101.
\(a.\dfrac{2}{3}-\dfrac{5}{7}.\dfrac{14}{25}=\dfrac{2}{3}-\dfrac{2}{5}=\dfrac{10}{15}-\dfrac{6}{15}=\dfrac{14}{15}\)
\(b.\dfrac{-2}{5}.\dfrac{5}{8}+\dfrac{5}{8}.\dfrac{3}{5}=\dfrac{5}{8}.\left(\dfrac{-2}{5}+\dfrac{3}{5}\right)=\dfrac{5}{8}.\dfrac{1}{5}=\dfrac{1}{8}\)
\(c.25\%-1\dfrac{1}{2}+0,5.\dfrac{12}{5}=\dfrac{1}{4}-\dfrac{3}{2}+\dfrac{6}{5}=-\dfrac{1}{20}\)
\(\dfrac{2x-1}{3}=\dfrac{2-x}{-2}\)
\(\Rightarrow-2\left(2x-1\right)=3\left(2-x\right)\)
\(\Rightarrow-4x+2=6-3x\Rightarrow x=-4\)
`x^3 - 1 = 124`
`x^3 = 124 + 1`
`x^3 = 125`
`x^3 = 5^3`
`→ x = 5`
Vậy `x = 5`
♪
x^3-1=124
x^3=124+1
x^3=125
x^3=5^3
vì 3=3
nên x=5