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a, x2 + 1 = 82
x2 = 82 - 1
x = \(\sqrt{81}\) = 9
b, x2 + \(\dfrac{7}{4}=\dfrac{23}{4}\)
x2 = \(\dfrac{23}{4}-\dfrac{7}{4}\)
x = \(\sqrt{4}=2\)
c, (2x + 3)2 = 25
(2x + 3) = \(\sqrt{25}\)
2x = 5 - 3
x = 2 : 2 = 1
d, (x + 5)3 = -64
(x + 5) = \(\sqrt[3]{-64}\)
x = (- 4) + (- 5) = -9
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a) \(4.\left(-\dfrac{1}{2}\right)^3-2.\left(-\dfrac{1}{2}\right)^2+3.\left(-\dfrac{1}{2}\right)+1\)
\(=4.\left(-\dfrac{1}{8}\right)-2.\dfrac{1}{4}+3.\left(-\dfrac{1}{2}\right)+1\)
\(=-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{3}{2}+1\)
\(=-\dfrac{3}{2}\)
b) \(8.\sqrt{9}-\sqrt{64}\)
\(=8.3-8\)
\(=24-8\)
\(=16\)
c) \(\sqrt{\dfrac{9}{16}}+\dfrac{25}{46}:\dfrac{5}{23}-\dfrac{7}{4}\)
\(=\dfrac{3}{4}+\dfrac{5}{2}-\dfrac{7}{4}\)
\(=-1+\dfrac{5}{2}\)
\(=\dfrac{3}{2}\)
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e: \(=\dfrac{5^{30}\cdot3^{20}}{3^{15}\cdot5^{30}}=3^5=243\)
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a)\(x^{23}=64.x^{20}\)
\(\Leftrightarrow\frac{x^{23}}{x^{20}}=64\)
\(\Leftrightarrow x^3=64\Rightarrow x=4\)
b)\(\left(4x-3\right)^4=3-4x\)
\(\Leftrightarrow\left(3-4x\right)^4=3-4x\)
\(\Leftrightarrow\left(3-4x\right)^3=1\)
\(\Leftrightarrow3-4x=1\)
\(\Leftrightarrow x=\frac{1}{2}\)
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\(1,\Rightarrow4^{x+1}=4^{3x}\\ \Rightarrow x+1=3x\\ \Rightarrow2x=1\\ \Rightarrow x=\dfrac{1}{2}\\ 2,\Rightarrow5x-2x=10+10x\\ \Rightarrow7x=-10\\ \Rightarrow x=-\dfrac{10}{7}\)
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`a,`\(2^x -15= 2^4+1\)
`-> 2^x-15=17`
`-> 2^x=17+15`
`-> 2^x=32`
`-> 2^x=2^5`
`-> x=5`
`b,` Có phải đề là \(\dfrac{x+1}{65}+\dfrac{x+2}{64}=\dfrac{x+3}{63}+\dfrac{x+4}{62}\) ?
`=>`\(\dfrac{x+1}{65}+1+\dfrac{x+2}{64}+1=\dfrac{x+3}{63}+1+\dfrac{x+4}{62}+1\)
`=>`\(\dfrac{x+1+65}{65}+\dfrac{x+2+64}{64}-\dfrac{x+3+63}{63}-\dfrac{x+4+62}{62}=0\)
`=>`\(\dfrac{x+66}{65}+\dfrac{x+66}{64}-\dfrac{x+66}{63}-\dfrac{x+66}{62}=0\)
`=>`\(\left(x+66\right)\left(\dfrac{1}{65}+\dfrac{1}{64}-\dfrac{1}{63}-\dfrac{1}{62}\right)=0\)
Mà `1/65+1/64-1/63-1/62 \ne 0`
`-> x+66=0`
`-> x=-66`
(23 : 4). 2x+1 = 64
=> (8 : 4) . 2x+1 = 64
=> 2.2x+1 = 64
=> 2x+1 = 32
=> 2x+1 = 25
=> x + 1 = 5 => x = 4
Vậy x = 4
\(\left(2^3\div4\right).2^{\left(x+1\right)}=64\Leftrightarrow\left(8\div4\right).2^x.2^1=2^6\)
\(\Leftrightarrow2^1.2^x.2^1=2^2.2^x=2^6\Leftrightarrow2^{\left(2+x\right)}=2^6\)
\(\Leftrightarrow2+x=6\Leftrightarrow x=6-2=4\)
Vậy \(x=4\)