5m²72m²=???m²

Máy bn giúp mình với làm ơn

Alo

Ta sẽ lần lượt chứng minh:\(\frac{a}{b}\)<\(\frac{5a+2c}{5b+2d}\)và \(\frac{5a+2c}{5b+2d}\)<\(\frac{c}{d}\)

Ta có: \(\frac{a}{b}\)<\(\frac{5a+2c}{5b+2d}\)

\(\Leftrightarrow\)a(5b+2d)<b(5a+2c)

\(\Leftrightarrow\)5ab+2ad<5ab+2bc

\(\Leftrightarrow\)2ad<2bc\(\Leftrightarrow\)ad<bc\(\Leftrightarrow\)\(\frac{a}{b}\)<\(\frac{c}{d}\)(đúng theo giả thiết)

Do vậy:\(\frac{a}{b}\)<\(\frac{5a+2c}{5b+2d}\)

Với lập luận tương tự ta cũng chứng minh được \(\frac{5a+2c}{5b+2d}\)<\(\frac{c}{d}\)

Vậy \(\frac{a}{b}\)<\(\frac{5a+2c}{5b+2d}\)<\(\frac{c}{d}\)

a)a/b=c/d=a+b/c+d=a-b/c-d(tc day ti so bang nhau)

=>a+b/a-b=c+d/c-d

b)a/b=c/d=>5a/5b=2c/2d=5a+2c/5c+2d(*) va a/b=4c/4d=a-4c/c-4d(**)

c)a/b=c/d=a+b/c+d=>(a/b)^2=ab/cd=(a+b/c+d)^2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=kb;c=kd\)

\(\Rightarrow\frac{5a+5b}{5b}=\frac{5b\left(k+1\right)}{5b}=k+1\)

\(\frac{c^2+cd}{cd}=\frac{k^2d^2+kd^2}{kd^2}=\frac{kd^2\left(k+1\right)}{kd^2}=k+1\)

\(\Rightarrow\frac{5a+5b}{5b}=\frac{c^2+cd}{cd}\)
 

\(\)\(\frac{5a+5b}{5b}=\frac{5a}{5b}+\frac{5b}{5b}=\frac{a}{b}+1\)

\(\frac{c^2+cd}{cd}=\frac{c^2}{cd}+\frac{cd}{cd}=\frac{c}{d}+1\)

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{b}+1=\frac{c}{d}+1\Rightarrow\frac{5a+5b}{5b}=\frac{c^2+cd}{cd}\)

\(\Rightarrowđpcm\)

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

=> a= b.k ; c= d.k

\(\frac{5a+5b}{5b}=\frac{5a}{5b}+\frac{5b}{5b}=\frac{a}{b}+1=\frac{b.k}{b}+1=k+1\left(1\right)\)

\(\frac{c^2+cd}{cd}=\frac{\left(d.k\right)^2}{cd}+\frac{cd}{cd}=\frac{d^2.k^2}{d.k.d}+1=\frac{d.k}{d}+1=k+1\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\Rightarrowđpcm\)

Ta có : \(A=5a+5a=5\left(a+b\right)\)

- Thay \(a+b=5\) vào A ta được :

\(A=5.5=25\)

Ta có : \(B=13a+5b+13b+5a\)

\(=13\left(a+b\right)+5\left(a+b\right)\)

\(=18\left(a+b\right)\)

- Thay \(a+b=5\) vào B ta được :

\(B=18.5=90\)

Ta có : \(C=5a+16b+4b+15a\)

\(=20a+20b\)

\(=20\left(a+b\right)\)

- Thay \(a+b=5\) vào C ta được :

\(C=20.5=100\)

Ta có : \(D=13a+19b+4a-2b\)

\(=17a+17b\)

\(=17\left(a+b\right)\)

- Thay \(a+b=5\) vào D ta được :

\(D=17.5=85\)