Question

Bài 3. Tìm x:

a) (3 – x)^2 – x(x – 4) = 2x – 5

b) x^2 – 2x + 1 = 25x^2

c) 4x^2 – 4x = 24

Answer 1

b) x² - 2x + 1 = 25x²

<=> (x - 1)² - 25x² = 0

<=> (x - 1 - 5x)(x - 1 + 5x)  = 0

<=> (-4x - 1)(6x - 1) = 0

<=> \(\orbr{\begin{cases}-4x-1=0\\6x-1=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=-\frac{1}{4}\\x=\frac{1}{6}\end{cases}}\)

Answer 2

c) 4x² - 4x = 24

<=> x² - x - 6 = 0

<=> x² - 3x + 2x - 6 = 0

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

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

<=> \(\orbr{\begin{cases}x+2=0\\x-3=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)

Answer 3

a) (3 - x)² - x(x - 4) = 2x - 5

<=> x² - 6x + 9-  x² + 4x = 2x - 5

<=> -2x + 9 = 2x - 5

<=> 2x + 2x = 9 + 5

<=> 4x = 14

<=> x = 7/2