Question

Giải pt:

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

b, \(\sqrt{22-x}\) - \(\sqrt{10-x}\) = 2

Answer 1

Co :\(\sqrt{x^2+x-1}=2-x\) (\(x\le\frac{-1-\sqrt{5}}{2}\);\(\frac{-1+\sqrt{5}}{2}\le x\le2\))

\(\Leftrightarrow x^2+x-1=4-4x+x^2\)
\(\Leftrightarrow5x=5\)
\(\Leftrightarrow x=1\) (thoa man DKXD ) 2 .\(\sqrt{22-x}+\sqrt{x-20}=2\) (\(20\le x\le22\))   Xet VT :\(\left(\sqrt{22-x}+\sqrt{x-20}\right)^2\le2\left(22-x+x-20\right)=4\)   \(\Leftrightarrow\sqrt{22-x}+\sqrt{x-20}\le2\)   \(\Rightarrow\)de thoa man PT \(\Leftrightarrow VT=VP=2\)
\(\Leftrightarrow\sqrt{22-x}=\sqrt{x-20}\)
\(\Leftrightarrow22-x=x-20\)
\(\Leftrightarrow x=21\left(thoamanDKXD\right)\)