Tim x y z x/2=7/3; 2y=3z và x+y+z=49 2x=3y; 4y=3z và x-y+z=21

thai.tom000

2 năm trước

Loga Sinh Học lớp 12

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minhy1064

Bạn tham khảo nhé!
$a)$ $\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$ $;$ $2y$ $=$ $3z$ và $x$ $+$ $y$ $+$ $z$ $=$ $49$
Đổi : $2y$ $=$ $3z$ $→$ $\dfrac{y}{3}$ $=$ $\dfrac{z}{2}$
Ta có : $\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$ (1)
Ta có : $\dfrac{y}{3}$ $=$ $\dfrac{z}{2}$ (2)
Từ (1) và (2) $→$ $\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$ $=$ $\dfrac{z}{2}$
Áp dụng t/c dãy tỉ số $=$ nhau ta có :
$\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$ $=$ $\dfrac{z}{2}$ $=$ $\dfrac{x+y+z}{2+3+2}$ $=$ $\dfrac{49}{7}$ $=$ $7$
$→$ $\dfrac{x}{2}$ $=$ $7$ $→$ $x$ $=$ $14$
và $\dfrac{y}{3}$ $=$ $7$ $→$ $y$ $=$ $21$
và $\dfrac{z}{2}$ $=$ $7$ $→$ $z$ $=$ $14$
$b)$ $2x$ $=$ $3y$ $;$ $4y$ $=$ $3z$ và $x$ $-$ $y$ $+$ $z$ $=$ $21$
Đổi : $2x$ $=$ $3y$ $→$ $\dfrac{x}{3}$ $=$ $\dfrac{y}{2}$
Đổi : $4y$ $=$ $3z$ $→$ $\dfrac{y}{3}$ $=$ $\dfrac{z}{4}$
Ta có : $\dfrac{x}{3}$ $=$ $\dfrac{y}{2}$
$→$ $\dfrac{x}{9}$ $=$ $\dfrac{y}{6}$ (1)
Ta có : $\dfrac{y}{3}$ $=$ $\dfrac{z}{4}$
$→$ $\dfrac{y}{6}$ $=$ $\dfrac{z}{8}$ (2)
Từ (1) và (2) $→$ $\dfrac{x}{9}$ $=$ $\dfrac{y}{6}$ $=$ $\dfrac{z}{8}$
Áp dụng t/c dãy tỉ số $=$ nhau ta có :
$\dfrac{x}{9}$ $=$ $\dfrac{y}{6}$ $=$ $\dfrac{z}{8}$ $=$ $\dfrac{x-y+z}{9-6+8}$ $=$ $\dfrac{21}{11}$ $=$ $\dfrac{21}{11}$
$→$ $\dfrac{x}{9}$ $=$ $\dfrac{21}{11}$ $→$ $x$ $=$ $\dfrac{189}{11}$
và $\dfrac{y}{6}$ $=$ $\dfrac{21}{11}$ $→$ $y$ $=$ $\dfrac{126}{11}$
và $\dfrac{z}{8}$ $=$ $\dfrac{21}{11}$ $→$ $z$ $=$ $\dfrac{168}{11}$
$FbBinhne2k88$

Vote (0) Phản hồi (0) 2 năm trước

thangthang662008

a) Hình như sai đề em ạ, mong em xem lại

b) 2x= 3y; 4y=3z và x-y+z=21

Đổi: 2x= 3y => x/3= y/2

Đổi: 4y= 3z => y/3= z/4

Từ: x/3= y/2; y/3= z/4

x/3= y/2 => x/9= y/6

y/3= z/4 => y/6= z/8

=> x/9= y/6= z/8

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

x/9= y/6= z/8= x-y+z/9-6+8= 21/11

Do đó: x/9= 21/11 => x= 9.21/11= 189/11

y/6= 21/11 => y= 6.21/11= 126/11

z/8= 21/11 => z= 8.21/11= 168/11

Vậy x= 189/11; y= 126/11; z= 168/11

Vote (0) Phản hồi (0) 2 năm trước

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