Question

Radical x+2 plus radical 3-x egal 3

Answer 1

$\sqrt{x+2}+ \sqrt{3-x}=3 \\ x+2+3-x+2 \sqrt{(x+2)(3-x)}=9 \\ 2 \sqrt{-x^2+x+6}=4 \\ \sqrt{-x^2+x+6}=2 \\ - x^{2} +x+6=4 \\ x^{2} -x-2=0 \\ x=-1;x=2$
verificam daca x=-1  si x=2 sunt  solutii ale ecuatiei
$\sqrt{-1+2}+ \sqrt{3-(-1)}=1+2=3 \\ \sqrt{2+2}+ \sqrt{3-2}=2+1=3$