Question

Determinati x din proportia x supra 2√5+3 = 2√5 -3 supra 11 .

Answer 1

$\displaystyle \frac{x}{2 \sqrt{5}+3}= \frac{ 2 \sqrt{5}-3}{11} \Rightarrow x= \frac{(2 \sqrt{5}+3)( 2 \sqrt{5}-3)}{11} = \frac{(2 \sqrt{5})^2-3^2}{11}= \\ \\ \\ = \frac{20-9}{11} = \frac{11}{11}=1. \\ \\ \underline{Solutie}: \boxed{x=1}~.$

Answer 2

Facem produsul mezilor si extrmilor si obtinem : 
(2√5+3)(2√5-3)=11*x----->20-9=11x--->11=11x|:11-->x=1