Bài 7: Tỉ lệ thức

Đặt a/b=c/d=k

=>a=bk; c=dk

a: \(\dfrac{3a+2b}{a}=\dfrac{3bk+2b}{bk}=\dfrac{3k+2}{k}\)

\(\dfrac{3c+2d}{c}=\dfrac{3dk+2d}{dk}=\dfrac{3k+2}{k}\)

Do đó: \(\dfrac{3a+2b}{a}=\dfrac{3c+2d}{c}\)

b: \(\dfrac{2a-3b}{b}=\dfrac{2bk-3b}{b}=2k-3\)

\(\dfrac{2c-3d}{d}=\dfrac{2dk-3d}{d}=2k-3\)

Do đó: \(\dfrac{2a-3b}{b}=\dfrac{2c-3d}{d}\)

c: \(\dfrac{a}{a-2b}=\dfrac{bk}{bk-2b}=\dfrac{k}{k-2}\)

\(\dfrac{c}{c-2d}=\dfrac{dk}{dk-2d}=\dfrac{k}{k-2}\)

Do đó: \(\dfrac{a}{a-2b}=\dfrac{c}{c-2d}\)

2x^2-3x+5

=2(x^2-3/2x+5/2)

=2(x^2-2*x*3/4+9/16+31/16)

=2(x-3/4)^2+31/8>=31/8>0 với mọi x

=>2x^2-3x+5 không có nghiệm

a: Trung bình nhân là: \(\sqrt{4\cdot16}=8\)

b: Trung bình nhân là: \(\sqrt{27\cdot\dfrac{4}{3}}=\sqrt{36}=6\)

b: x/y=-3/7

=>x/-3=y/7

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{-3}=\dfrac{y}{7}=\dfrac{x-y}{-3-7}=\dfrac{-40}{-10}=4\)

=>x=-12; y=28

d: Đặt x/3=y/4=k

=>x=3k; y=4k

xy=48

=>3k*4k=48

=>12k^2=48

=>k^2=4

TH1: k=2

=>x=6; y=8

TH2: k=-2

=>x=-6; y=-8

\(8\dfrac{1}{3}:11\dfrac{2}{3}=13:2x\)

\(\Rightarrow\dfrac{25}{3}:\dfrac{35}{3}=13:2x\)

\(\Rightarrow\dfrac{5}{7}=13:2x\)

\(\Rightarrow2x=13:\dfrac{5}{7}\)

\(\Rightarrow2x=\dfrac{91}{5}\)

\(\Rightarrow x=\dfrac{91}{5}:2\)

\(\Rightarrow x=\dfrac{91}{10}\)

\(\left(x-1\right):24,5=5:8,75\)

\(\Rightarrow8,75\cdot\left(x-1\right)=24,5\cdot5\)

\(\Rightarrow8,75\cdot\left(x-1\right)=122,5\)

\(\Rightarrow x-1=14\)

\(\Rightarrow x=14+1\)

\(\Rightarrow x=15\)

\(\dfrac{x}{18}=\dfrac{-3}{3,6}\)

\(\Rightarrow3,6x=-3\cdot18\)

\(\Rightarrow3,6x=-54\)

\(\Rightarrow x=\dfrac{-54}{3,6}\)

\(\Rightarrow x=-15\)

a)

n = 20 tức n chẵn.

Khi n chẵn: \(A=-4.\dfrac{n}{2}=-4.\dfrac{20}{2}=-40\)

b)

Khi n chẵn:

\(A=-4.\dfrac{n}{2}=-2n\)

Khi n lẽ:

\(A=1+\dfrac{4\left(n-1\right)}{2}=1+2\left(n-1\right)=1+2n-2=2n-1\)

cảm ơn HaNa nhiều nha =)

help me

Đặt x/5=y/2=k

=>x=5k; y=2k

3x^2-2y^2=268

=>3*25k^2-2*4k^2=268

=>k^2=4

TH1: k=2

=>x=10; y=4

TH2: k=-2

=>x=-10; y=-4

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

Thay vào \(x^2+y^2=325\), ta có: 

\(\dfrac{4}{9}y^2+y^2=325\\ \Leftrightarrow\dfrac{13}{9}y^2=325\\ \Leftrightarrow y^2225\\ \Leftrightarrow\left[{}\begin{matrix}y=15\Rightarrow x=10\\y=-15\Rightarrow x=-10\end{matrix}\right.\)

Đặt x/2=y/3=k

=>x=2k; y=3k

x^2+y^2=325

=>13k^2=325

=>k^2=25

TH1: k=5

=>x=10; y=15

TH2: k=-5

=>x=-10; y=-15

1/2 = 2/4 = 4/8 = 8/16 = 16/32

1/4 = 2/8 = 4/16 = 8/32

1/8 = 2/16 = 4/32

=> 19 tỉ lệ thức