Question

Bài : Giải các phương trình sau 
a) \(\sqrt{\left(x-1\right)^2-\left(x^2-3\right)}\) = 3
b) \(\dfrac{x+3}{x}\) + \(\dfrac{x-3}{x-2}\) =2

Answer 1

\(a,\sqrt{\left(x-1\right)^2-\left(x^2-3\right)}=3\)

\(\Leftrightarrow\left(x-1\right)^2-\left(x^2-3\right)=9\)

\(\Leftrightarrow x^2-2x+1-x^2+3=9\)

\(\Leftrightarrow4-2x=9\)

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

\(b,\dfrac{x+3}{x}+\dfrac{x-3}{x-2}=2\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(2x-2\right)}{x\left(x-2\right)}=2\)

\(\Leftrightarrow\left(x-3\right)\left(2x-2\right)=2x\left(x-2\right)\)

\(\Leftrightarrow2x^2-8x+6=2x^2-4x\)

\(\Leftrightarrow-4x=-6\)

\(\Leftrightarrow x=1,5\)

Answer 2

a) \(\sqrt{(x-1)^{2}- x^2-3)}=3\)

\(\Leftrightarrow \sqrt{x^2-2x+1-x^2+3}=3\)

\(\Leftrightarrow \sqrt{4-2x}=3\)

\(\Leftrightarrow 4-2x = 9\)

\(\Leftrightarrow 2x=-5\)

\(\Leftrightarrow x=-2.5\)

Vậy S = {-2.5}