Question

[Noob]

Bài 3,4 nhé

Answer 1

[Akai Haruma]

Bài 3:

a. $\frac{x-3}{x+5}=\frac{5}{7}$

$\Rightarrow 7(x-3)=5(x+5)$

$7x-21=5x+25$

$2x=46$

$x=23$

b.

$\frac{7}{x-1}=\frac{x+1}{9}$

$7.9=(x-1)(x+1)$

$63=x^2-1$

$x^2=64=8^2=(-8)^2$

$\Rightarrow x=\pm 8$

c.

$\frac{x+4}{20}=\frac{5}{x+4}$

$(x+4)^2=20.5=100=10^2=(-10)^2$

$\Rightarrow x+4=\pm 10$

$\Rightarrow x=6$ hoặc $x=-14$

d.

$\frac{x-1}{x+2}=\frac{x-2}{x+3}$
$(x-1)(x+3)=(x+2)(x-2)$

$x^2+2x-3=x^2-4$

$2x-3=-4$

$2x=-1$

$x=\frac{-1}{2}$

Answer 2

[Akai Haruma]

Bài 4:

a. Áp dụng TCDTSBN:
$\frac{x}{7}=\frac{y}{13}=\frac{x+y}{7+13}=\frac{40}{20}=2$

$\Rightarrow x=7.2=14; y=13.2=26$

b. Áp dụng TCDTSBN:
$\frac{3}{x}=\frac{7}{y}=\frac{3-7}{x-y}=\frac{-4}{-16}=\frac{1}{4}$

$\Rightarrow x=3.4=12; y=7.4=28$

c. Áp dụng TCDTSBN:

$2x=3y=5z$

$=\frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{5}}$

$=\frac{x+y-z}{\frac{1}{2}+\frac{1}{3}-\frac{1}{5}}=\frac{95}{\frac{19}{30}}=150$

$\Rightarrow x=\frac{1}{2}.150=75; y=\frac{1}{3}.150=50; z=\frac{1}{5}.150=30$

d. Áp dụng TCDTSBN:

$\frac{x}{2}=\frac{y}{3}=\frac{x+y}{2+3}=\frac{-15}{5}=-3$

$\Rigghtarrow x=2(-3)=-6; y=3(-3)=-9$