Question

giải phương trình:

p/s: bạn nào làm đc câu nào thì làm, ko nhất thiết phải làm hết

a,\(\sqrt{\left(x-1\right)^2}=5\)

b,\(3+\sqrt{x}=5\)

c,\(\sqrt{x^2-2x+1}=x-1\)

d,\(\sqrt{x^2-10x+25}=x+3\)

e,\(\sqrt{x-5}+\sqrt{5-x}=1\)

Answer 1

a, \(\sqrt{\left(x-1\right)^2}=5\Rightarrow\left(x-1\right)=\left\{5;-5\right\}\Leftrightarrow\hept{\begin{cases}x-1=5\Rightarrow x=6\\x-1=-5\Rightarrow x=-4\end{cases}}\)

b,\(3+\sqrt{x}=5\Rightarrow\sqrt{x}=2\Rightarrow x=4\)

c,\(\sqrt{x^2-2x+1}=x-1\Rightarrow\sqrt{\left(x-1\right)^2}=x-1\Rightarrow x-1=\left\{x-1;-\left(x-1\right)\right\}\)

\(\Leftrightarrow\hept{\begin{cases}x-1=x-1\Rightarrow x\in R\\x-1=-\left(x-1\right)\Rightarrow x-1=-x+1\Rightarrow x+x=1+1\Rightarrow2x=2\Rightarrow x=1\end{cases}}\)

Vậy x = 1

d, \(\sqrt{x^2-10x+25}=x+3\Rightarrow\sqrt{\left(x-5\right)^2}=x+3\Rightarrow x-5=\left\{x+3;-\left(x+3\right)\right\}\)

\(\Leftrightarrow\hept{\begin{cases}x-5=x+3\Rightarrow x-x=3+5\Rightarrow0x=8\left(loai\right)\\x-5=-\left(x+3\right)\Rightarrow x-5=-x-3\Rightarrow x+x=-3+5\Rightarrow2x=2\Rightarrow x=1\left(chon\right)\end{cases}}\)

Vậy x = 1