Conditii de existenta
x+3>0 x>-3
x>0
x+8>0 x>-8
Observam ca avem aceeasi baza
Deci vom avea
[tex]5+\sqrt{x+3} +\sqrt{x} =5+\sqrt{x+8} \ \ |-5\\\\\sqrt{x+3} +\sqrt{x}=\sqrt{x+8} \ \ \ |^2\\x+3+2\sqrt{x(x+3)} +x=x+8\\\\2\sqrt{x(x+3)}=5-x\ \ \ |^2\\\\4x(x+3)=25-10x+x^2\\\\4x^2+12x-25+10x-x^2=0\\\\3x^2+22x-25=0[/tex]
Δ=484+300=784
[tex]x_1=\frac{-22+28}{6} =1\\\\x_2=\frac{-22-28}{6} =-\frac{25}{3} < 0\ nu[/tex]
