\(2^{x+2}-2^x=96\)

\(2^x.\left(2^2-1\right)=96\)

\(2^x.3=96\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

\(2^{x+2}-2^x=96\)   

\(2^x\left(2^2-1\right)=96\)   

\(2^x\left(4-1\right)=96\)   

\(2^x\cdot3=96\)   

\(2^x=96:3\)   

\(2^x=32\)   

\(2^x=2^5\)   

\(x=5\)

2^x + 2^{x + 1} = 96

=> 2^x(1+2)=96

=>2^x.3=96

=> 2^x=96:3=32

=> 2^x=32=2⁵

=> x=5

Vây x=5

2^x + 2^x+1 = 96

2^x + 2^x . 2 =96

2^x . (1 + 2)= 96

2^x. 3 = 96

2^x    = 96:3=32

mà 32 = 2⁵ => x = 5

Vậy x = 5 

2^x+2^x+1=96

2^x+2^x.2=96

2^x(1+2)=96

2^x=96:3=32=2⁵

Suy ra x=5

x = 5 nha bạn

2^x+2^x.2=96

2^x(1+2)=96

2^x.3=96

2^x=96:3

2^x=32

2^x=2⁵

x=5

Ta có: 

\(\frac{x+1}{98}+1+\frac{x+2}{97}+1=\frac{x+3}{96}+1+\frac{x+4}{95}+1\)

\(\frac{x+1}{98}+\frac{98}{98}+\frac{x+2}{97}+\frac{97}{97}=\frac{x+3}{96}+\frac{96}{96}+\frac{x+4}{95}+\frac{95}{95}\)

\(\frac{x+99}{98}+\frac{x+99}{97}=\frac{x+99}{96}+\frac{x+99}{95}\)

\(\frac{x+99}{98}+\frac{x+99}{97}-\frac{x+99}{96}-\frac{x+99}{95}=0\)

\(\left(x+99\right)\left(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}\right)=0\)

Vì: \(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}\ne0\)nên x+99=0

=> x=-99

Ai tra loi nhanh nhat minh se cho

4x + (1/99+2/98+3/97 + 4/96)=-4

4x=-4 - (1/99+2/98+3/97 + 4/96)

4x=

\(\frac{2}{x}=\frac{3}{y}\Rightarrow x=\frac{2y}{3}\)

Thay vào x . y, ta được:

 \(x\cdot y=\frac{2y}{3}\cdot y=\frac{2y^2}{3}=96\)

=>  \(2y^2=96\cdot3=288\Rightarrow y^2=\frac{288}{2}=144\)

=>  \(y=\sqrt{144}=12\)  hoặc   \(y=-12\)

Vậy x = 8; y = 12    hoặc    x = -8 ; y = -12  

\(\frac{2}{x}=\frac{3}{y}=>\frac{2}{x}.\frac{3}{y}=\frac{3}{y}.\frac{3}{y}=>\frac{6}{xy}=\frac{9}{y^2}=>\frac{6}{96}=\frac{9}{y^2}=>\frac{1}{16}=\frac{9}{y^2}\)

\(=>y^2=9:\frac{1}{16}=144=12^2=\left(-12\right)^2\)

=>y=12,-12

Với y=12=>x=96:12=8

Với y=-12=>x=96:(-12)=-8

Vậy x=-8,y=-12

       x=8,y=12

Từ 2/x = 3/y ta có4/x² = 2/x . 3/y = 6/xy = 6/96 = 1/16

                       =>x=+-8

Nếu x = 8 thì y = 96 : 8 = =12

Nếu x = -8 thì y = 96 : (-8) = -12

de ot giai violympic ma cau ko bit lam bai nay a. Bai nay cach lam dai Khi nao ranh to ghi cho

a) \(2^{x+2}-2^2=96\)

 <=> \(2^x.2^2-2^x=96\)

 <=> \(2^x\left(4-1\right)=96\)

<=> \(3.2^x=96\)

<=> \(2^x=32\)

<=> \(2^x=2^5\)

<=> x = 5 

b, \(x-\left(\frac{50x}{100}+\frac{25x}{200}\right)=11\frac{1}{4}\)

\(\Rightarrow x-\left(\frac{1x}{2}+\frac{1x}{8}\right)=\frac{45}{4}\)

\(\Rightarrow x-\left(\frac{4x}{8}+\frac{1x}{8}\right)=\frac{45}{4}\)

\(\Rightarrow x-\frac{5x}{8}=\frac{45}{4}\)

\(\Rightarrow\frac{8x}{8}-\frac{5x}{8}=\frac{45}{4}\)

\(\Rightarrow\frac{3x}{8}=\frac{45}{4}\Rightarrow x=\frac{45}{4}\div\frac{3}{8}=30\)

Vậy x = 30