Question

Answer 1

a) \(\Rightarrow x\left(x+5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)

b) \(\Rightarrow\left(x+1\right)\left(x+1-1\right)=0\)

\(\Rightarrow x\left(x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)

c) \(\Rightarrow x\left(x^2+1\right)=0\)

\(\Rightarrow x=0\) (do \(x^2+1\ge1>0\))

d) \(\Rightarrow\left(x-5\right)^2=0\)

\(\Rightarrow x=5\)

e) \(\Rightarrow x\left(x^2-4\right)=0\)

\(\Rightarrow x\left(x-2\right)\left(x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)

f) \(\Rightarrow\left(3x-2\right)\left(x^2+4\right)=0\)

\(\Rightarrow x=\dfrac{2}{3}\) (do \(x^2+4\ge4>0\))