Question

Tìm x, biết:

a) x\(^2\) – 4x + 4 = 25

b) (5 – 2x)\(^2\) – 16 = 0 

Answer 1

a: =>(x-2)²=25

=>x-2=5 hoặc x-2=-5

=>x=7 hoặc x=-3

b: =>(2x-5)²=16

=>2x-5=4 hoặc 2x-5=-4

=>2x=9 hoặc 2x=1

=>x=9/2 hoặc x=1/2

Answer 2

a) \(x^2-4x+4=25\)

\(\Rightarrow\left(x-2\right)^2=\left(\pm5\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x-2=5\\x-2=-5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)

b) \(\left(5-2x\right)^2-16=0\)

\(\Rightarrow\left(5-2x\right)^2-4^2=0\)

\(\Rightarrow\left(5-2x-4\right)\left(5-2x+4\right)=0\)

\(\Rightarrow\left(1-2x\right)\left(9-2x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}1-2x=0\\9-2x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{9}{2}\end{matrix}\right.\)