Question

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

Answer 1

\(\Leftrightarrow1-x+2+x-2\sqrt{\left(1-x\right)\left(2+x\right)}=1\)

=>\(2\sqrt{\left(1-x\right)\left(2+x\right)}=3-1=2\)

=>(1-x)(2+x)=1

=>2+x-2x-x^2=1

=>-x^2-x+2-1=0

=>-x^2-x+1=0

=>x^2+x-1=0

=>\(x=\dfrac{-1\pm\sqrt{5}}{2}\)