\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.....\dfrac{31}{64}\)
\(=\dfrac{2.3.....31}{\left(2.3.4.....31\right).\left(2.2.2.....2\right).2^6}\)(Ở phần 2 . 2 . 2 . ... . 2 có 30 số 2)
\(=\dfrac{1}{2^{30+6}}=\dfrac{1}{2^{36}}\)
\(\Rightarrow\dfrac{1}{2^{36}}=2^x\)
\(\Rightarrow2^{36}=2^{0-x}\)
\(\Rightarrow36=0-x\)
\(\Rightarrow x=-36\)
1/4.2/6.3/8.4/10.5/12.......30/62.31/64=2^x
a,\(\dfrac{1+2y}{18}=\dfrac{1+4y}{24}=\dfrac{1+6y}{+6x}\)
b, \(\dfrac{1+3y}{12}=\dfrac{1+5y}{5x}=\dfrac{1+7y}{4x}\)
c,\(\dfrac{x}{z+y+1}=\dfrac{y}{x+z+1}=\dfrac{z}{x+y-2}=x+y+z\left(x,y,zkhac0\right)\)
d, \(\dfrac{3x}{8}=\dfrac{3y}{64}=\dfrac{3z}{216}va2x^2+2y^2-z^2=1\)
Tìm x,y,z trong dãy tỉ số bằng nhau
1)\(\dfrac{3x}{8}=\dfrac{3y}{64}=\dfrac{3z}{216}\)và \(2x^2+2y^2.z^2=1\)
2) \(\dfrac{2x+1}{5}=\dfrac{4y-5}{9}=\dfrac{2x+4y-4}{7x}\)
3) \(\dfrac{x^3+y^3}{6}=\dfrac{x^3-2y^3}{4}\)và x6 . y6 =14
4) \(\dfrac{x+4}{6}=\dfrac{3y-1}{8}=\dfrac{3y-x-5}{x}\)
5) \(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\)và x.y.z=192
6)\(\dfrac{x-y}{3}=\dfrac{x+y}{13}=\dfrac{x.y}{200}\)
7)\(\dfrac{x+1}{2}=\dfrac{y-1}{3}=\dfrac{z+2}{4}=\dfrac{x+y+z+2}{2x+5}\)
8) \(\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\)và x.y = 1200
9)\(\dfrac{40}{x-30}=\dfrac{20}{y-15}=\dfrac{28}{z-21}\) và x.y.z = 22400
10)15x = -10y =6z và x.y.z = -30000
11) Cho\(\dfrac{x+1}{3}=\dfrac{y-2}{5}=\dfrac{2z+14}{9}\)và x+z=y
12) Cho \(\dfrac{x}{3}=\dfrac{y}{4}\)và \(\dfrac{y}{5}=\dfrac{z}{6}\).Tính M=\(\dfrac{2x+3y+4z}{3x+4y+5z}\)
Tìm x
A, ( x - 1 )^x+2 = ( x - 1 )^x+4
B, 1/4 × 2/6 × 3/8 × 4/10 × 5/12 ×....× 30/62 × 31/64 = 2^x
1/4×2/6×3/8×4/10×5/12×.....×30/62×1/64=2^x
Tìm x
\(\frac{x}{4}=\frac{y}{5}\&x+y=9\)
\(\frac{2x}{4}=\frac{6y}{12}=\frac{8z}{64}\&x+y+z=12\)
\(5x=4y,3y=5z\&x+y+z=11\)
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tìm x,y,z
a,\(\dfrac{12x-15y}{7}=\dfrac{20z-12x}{9}=\dfrac{15y-20z}{11}\) và x+y+z=48
b, x.( x+y+z)=-12 ; y.( x+y+z)=18;z.( x+y+z)=30
Tìm x, y, z :
a, \(\frac{x^3}{8}=\frac{y^3}{64}=\frac{z^3}{216}\) và x2+y2+z2=14
b, \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) và 2x+3y-z=50
c, 2x=3y=5z và x+y-z=95
Tìm các số x,y,z biết \(64^{x-1}:4^{x+1}=\left(256^x\right)^2\)
