Question

Tìm x

a) x^2 - 2x + 1 = 25

b) ( 5 - 2x )^ 2 + 1 = 25

giải nhanh dùm

Answer 1

Ta có : x² - 2x + 1 = 25

=> x² - 2.x.1 + 1² = 25

=> (x - 1)² = 25

Mà 25 = 5² ; (-5)²

=> \(\orbr{\begin{cases}\left(x-1\right)^2=5^2\\\left(x-1\right)^2=\left(-5\right)^2\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)

Vậy x = {-4;6}

Answer 2

b) (5 - 2x)² + 1 = 25

<=> (5 - 2x)² = 24 

\(\Rightarrow\orbr{\begin{cases}5-2x=\sqrt{24}\\5-2x=-\sqrt{24}\end{cases}}\Rightarrow\orbr{\begin{cases}2x=5-2\sqrt{6}\\2x=5+2\sqrt{6}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5-2\sqrt{6}}{2}\\x=\frac{5+2\sqrt{6}}{2}\end{cases}}\)