Question

Comparati :
x=radical din 2+ radical din 5 si y= radical din 7+ 1. Comparati patratele lor.

Answer 1

x=√2+√5
y=√7+1     

le ridicam la patrat pe amandoua relatiile de unde se vede clar ca x>y.
x²=2+5+2√10=7+2√10
y²=7+1+2√7=8+2√7
   
     x               y
7+2√10 ___ 8+2√7
7+6.32 ___ 8+5.27
13.32 > 13.27 =>x>y

Answer 2

$\sf x= \sqrt{2}+ \sqrt{5} } \\ \\ y= \sqrt{7}+1 \\ \\ x^2=(\sqrt{2}+ \sqrt{5})^2=2+5+2 \sqrt{10} \\ \\ y^2=( \sqrt{7}+1)^2=7+1+2 \sqrt{7} \\ \\ 7+2 \sqrt{10}~\boxed{=}~8+2 \sqrt{7} \\ \\7+2*3,1~\boxed{=}~8+2*2,6 \\ \\7+6,2~\boxed{=}~8+5,2 \\ \\ \boxed{\sf 13,2~=~13,2}$