giúp mik vs

A B C D E M F

a) Áp dụng định lý Talet vào tam giác ABC có DE//BC

\(\frac{AB}{BD}=\frac{AC}{CE}\Rightarrow\frac{CE}{BD}=\frac{AC}{AB}\)

mà BD=CF (gt) \(\Rightarrow\frac{CE}{CF}=\frac{AC}{AB}\left(1\right)\)

Ta có: DE//BC mà B \(\in\)BC

=> DE//MC

\(\Rightarrow\frac{MD}{MF}=\frac{CE}{CF}\left(2\right)\)

\(\left(1\right)\left(2\right)\Rightarrow\frac{MD}{MF}=\frac{AC}{AB}\left(đpcm\right)\)

b) BC=8cm, BD=5cm, DE=3cm

Áp dụng định lý Talet vào tam giác ABC có: DE//BC

\(\Rightarrow\frac{DF}{BC}=\frac{AD}{AB}=\frac{AE}{AC}\)

\(\Rightarrow\frac{DE}{BC}=\frac{AD}{AB}=\frac{AB-BD}{AB}\)

\(\Leftrightarrow\frac{AB-5}{AB}=\frac{3}{8}\)

<=> 3AB=8AB-40

<=> 5AB=40

<=> AB=8cm

AB=BC=8cm => Tam giác ABC cân (đpcm)

(2x² - 3x - 1)² - 3(2x² - 3x - 5) - 16 = 0

<=> 4x⁴ - 12x³ - x² + 15x = 0

<=> x(x + 1)(2x - 3)(2x - 5) = 0

<=> x = 0 hoặc x + 1 = 0 hoặc 2x - 3 = 0 hoặc 2x - 5 = 0

<=> x = 0 hoặc x = -1 hoặc x = 3/2 hoặc x = 5/2

\(\left(3x-1\right)^2-\left(x+3\right)\left(2x-1\right)=7\left(x+1\right)\left(x-2\right)-3x\)

\(\Leftrightarrow9x^2-6x+1-\left(2x^2+6x-x-3\right)=7\left(x^2-x-2\right)-3x\)

\(\Leftrightarrow7x^2-11x+4=7x^2-10x-14\)

\(\Leftrightarrow-x=-28\Leftrightarrow x=28\)

\(5x-24+4x^2+3x=4-6x+4x^2+2\)

\(5x-24+4x^2+3x-4-6x+4x^2+2=0\)

\(2x-26+8x^2=0\)

\(2x+8x^2=26\)

\(5x-4\left(6-x\right)\left(x+3\right)=\left(4-2x\right)\left(3-2x\right)+2\)

\(\Leftrightarrow5x-4\left(6x-x^2+18-3x\right)=\left(12-6x-8x+4x^2\right)+2\)

\(\Leftrightarrow5x-24x+4x^2-72+12x=14-14x+4x^2\)

\(\Leftrightarrow4x^2-72-7x=14-14x+4x^2\)

\(\Leftrightarrow7x=86\Leftrightarrow x=\frac{86}{7}\)

a) 6x² - 5x + 3 = 2x - 3x(2 - x)

<=> 6x² - 5x + 3 = 2x - 6x + 3x²

<=> 6x² - 5x + 3 = -4x + 3x²

<=> 6x² - 5x + 3 + 4x - 3x² = 0

<=> 3x² - x + 3 = 0

=> Pt vô nghiệm

b) 25x² - 9 = (5x + 3)(2x + 1)

<=> 25x² - 9 = 10x² + 5x + 6x + 3

<=> 25x² - 9 = 10x² + 11x + 3

<=> 25x² - 9 - 10x² - 11x - 3 = 0

<=> 15x² - 12 - 11x = 0

<=> 15x² + 9x - 20x - 12 = 0

<=> 3x(5x + 3) - 4(5x + 3) = 0

<=> (5x + 3)(3x - 4) = 0

<=> 5x + 3 = 0 hoặc 3x - 4 = 0

<=> x = -3/5 hoặc x = 4/3