Question

Giải phương trình:

a. \(\sqrt{\left(x-3\right)^2}=3-x\)

b. \(\sqrt{4x^2-20x+25}+2x=5\)

c. \(\sqrt{x-2\sqrt{x-1}}=\sqrt{x-1}-1\)

d. \(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\)

Answer 1

a.\(\sqrt{\left(x-3\right)^2}=3-x\)

\(\Leftrightarrow x-3=3-x\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=3\)

b.\(\sqrt{4x^2-20x+25}+2x=5\)

\(\Leftrightarrow\sqrt{\left(2x-5\right)^2}=5-2x\)

\(\Leftrightarrow2x-5=5-2x\)

\(\Leftrightarrow4x=10\)

\(\Leftrightarrow x=\dfrac{5}{2}\)

c.

d.\(\sqrt{x^2-\dfrac{1}{2}x+\dfrac{1}{16}}=\dfrac{1}{4}-x\)

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

\(\Leftrightarrow x-\dfrac{1}{4}=\dfrac{1}{4}-x\)

\(\Leftrightarrow x=\dfrac{1}{4}\)

Answer 2

a: =>|x-3|=3-x

=>x-3<=0

hay x<=3

b: =>|2x-5|=-2x+5

=>2x-5<=0

=>x<=5/2

c: =>|căn x-1-1|=căn x-1-1

=>căn x-1-1>=0

=>căn x-1>=1

=>x-1>=1

hay x>=2