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a, 3x+2 +3x = 90
3x . 32 + 3x = 90
3x. ( 32 + 1 ) = 90
3x . 10 =90
3x = 90 : 10
3x = 9
3x = 32
x = 2
1+2+3+......+x =210
(x+1) . x : 2= 210
(x+1) . x = 210 .2
(x+1) .x = 420
21 . 20 = 420
x = 20
a) \(2^{x-1}+2^{x+1}+2^{x+2}=104\)
=> \(2^{x-1}+2^x\cdot2+2^x\cdot2^2=104\)
=> \(2^x:2+2^x\cdot\left(2+2^2\right)=104\)
=> \(2^x\cdot\frac{1}{2}+2^x\cdot6=104\)
=> \(2^x\cdot\left(\frac{1}{2}+6\right)=104\Rightarrow2^x=104:\left(\frac{1}{2}+6\right)=104:\frac{13}{2}=16\)
=> \(x=4\)
a. x50 = x
\(\Rightarrow\)\(\left[\begin{array}{nghiempt}x=1\\x=-1\end{array}\right.\)
b. 125 = x3
Vì 53 =125 \(\Rightarrow\)x = 5
c.64 = x2
Vì 64 = 82 \(\Rightarrow\) x = 8
d.90 = 10 . 3x
3x= 90 : 10
3x = 9
Vì 32 = 9 \(\Rightarrow\)x = 2
a) \(\text{2(x-51)=2.2^2+20}\)
\(2\left(x-51\right)=2.4+20\)
\(2\left(x-51\right)=28\)
\(x-51=28\div2\)
\(x-51=14\)
\(x=14+51\)
\(\text{b)3.(x+1)-26=541}\)
\(3.\left(x+1\right)=541+26\)
\(3\cdot\left(x+1\right)=567\)
\(x+1=567\div3\)
\(x+1=189\)
\(x=189-1\)
\(x=188\)
\(x=65\)
\(\text{c)4(x-3)=7^2-1^10}\)
\(4\left(x-3\right)=49-1\)
\(4\left(x-3\right)=48\)
\(x-3=48\div4\)
\(x-3=12\)
\(x=12+3\)
\(x=15\)
\(\text{e)2x-138=2^3.3^2}\)
\(2x-138=8\cdot9\)
\(2x-138=72\)
\(2x=72+138\)
\(2x=210\)
\(x=210\div2\)
\(x=105\)
\(\text{f)(x-1)^4=16}\)
\(\left(x-1\right)^4=2^4\)
\(x-1=2\)
\(x=2+1\)
\(x=3\)
a: \(\dfrac{x}{x+3}=\dfrac{2}{5}\)
=>5x=2x+6
=>3x=6
hay x=2
b: \(\left(x+\dfrac{1}{2}\right)^2-\dfrac{1}{3}=\dfrac{1}{9}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\)
=>x+1/2=2/3 hoặc x+1/2=-2/3
=>x=1/6 hoặc x=-7/6
c: \(\left(x-\dfrac{1}{2}\right)^3+\dfrac{1}{4}=\dfrac{3}{8}\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{3}{8}-\dfrac{2}{8}=\dfrac{1}{8}\)
=>x-1/2=1/2
hay x=1
d: \(2^{x+3}=32\)
=>x+3=5
hay x=2
e: \(\Leftrightarrow3^x\left(3^2+1\right)=90\)
\(\Leftrightarrow3^x=9\)
hay x=2
Tui làm bài hình thôi nha.
O y x m n t
a/ Ta có: \(\hept{\begin{cases}\widehat{xOm}=\widehat{nOy}=90^0\left(gt\right)\\\widehat{nOm}:chung\end{cases}\Rightarrow\widehat{xOn}=\widehat{mOy}}\)
b/ Vì Ot là pgiác góc xOy => góc xOt = góc tOy
Mà: góc xOn = góc mOy (cmt)
=> góc nOt = góc tOm
=> Ot là phân giác góc nOm
b, \(\left(x+\frac{1}{2}\right)^2-\frac{1}{3}=\frac{1}{9}\)
\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2=\frac{4}{9}\)
\(\Leftrightarrow\left(x+\frac{1}{2}\right)^2=\left(\frac{2}{3}\right)^3\)
\(\Leftrightarrow x+\frac{1}{2}=\frac{2}{3}\Rightarrow x=\frac{1}{6}\)
c, \(\left(x-\frac{1}{2}\right)^3+\frac{1}{4}=\frac{3}{8}\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\frac{1}{8}\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{2}\right)^3\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{1}{2}\\x-\frac{1}{2}=-\frac{1}{2}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}\)
b,3x+2+3x=90
3x.32+3x=90
3x.(32+1)=90
3x.10=90
3x=90:10
3x=9