Question

Tìm x

a. x² - 12x - 2x + 24 = 0

b. x² - 5x - 24 = 0

c. 4x² - 12x - 7 = 0

d. x³ + 6x² + 12x + 8 = 0

e. (x + 2)² - x² + 4 = 0

f. 2(x + 5) = x² + 5x

m. 16(2x - 3)² - 25(x - 5)² = 0

n. x² - 6x + 4 = 0

Answer 1

a) \(x^2-12x-2x+24=0\)

\(\Leftrightarrow x\left(x-12\right)-2\left(x-12\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-12\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=12\\x=2\end{cases}}\)

b) \(x^2-5x-24=0\)

\(\Leftrightarrow\left(x^2+3x\right)-\left(8x+24\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x-8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=-3\\x=8\end{cases}}\)

c) \(4x^2-12x-7=0\)

\(\Leftrightarrow\left(4x^2-14x\right)+\left(2x-7\right)=0\)

\(\Leftrightarrow\left(2x-7\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{1}{2}\end{cases}}\)

d) \(x^3+6x^2+12x+8=0\)

\(\Leftrightarrow\left(x+2\right)^3=0\)

\(\Rightarrow x=-2\)

Answer 2

e) \(\left(x+2\right)^2-x^2+4=0\)

\(\Leftrightarrow4x+8=0\)

\(\Rightarrow x=-2\)

f) \(2\left(x+5\right)=x^2+5x\)

\(\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(2-x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=-5\\x=2\end{cases}}\)

m) \(16\left(2x-3\right)^2-25\left(x-5\right)^2=0\)

\(\Leftrightarrow\orbr{\begin{cases}8x-12=5x-25\\8x-12=25-5x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x=-13\\13x=37\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{13}{3}\\x=\frac{37}{13}\end{cases}}\)

n) \(x^2-6x+4=0\)

\(\Leftrightarrow\left(x-3\right)^2-5=0\)

\(\Leftrightarrow\left(x-3+\sqrt{5}\right)\left(x-3-\sqrt{5}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=3+\sqrt{5}\\x=3-\sqrt{5}\end{cases}}\)