Question

9x²+12x+4=0

x²+\(\dfrac{1}{4}\)=x

4-\(\dfrac{12}{x}\)+\(\dfrac{9}{x^2}\)=0

Answer 1

(a) \(9x^2+12x+4=0\)

\(\Leftrightarrow\left(3x+2\right)^2=0\Leftrightarrow3x+2=0\Leftrightarrow x=-\dfrac{3}{2}\)

 

(b) \(x^2+\dfrac{1}{4}=x\)

\(\Leftrightarrow x^2-x+\dfrac{1}{4}=0\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{2}\)

 

(c) \(4-\dfrac{12}{x}+\dfrac{9}{x^2}=0\left(x\ne0\right)\)

\(\Leftrightarrow\left(2-\dfrac{3}{x}\right)^2=0\Leftrightarrow2-\dfrac{3}{x}=0\Leftrightarrow x=\dfrac{3}{2}\)