Question

...........................................

Answer 1

Ridicam la patrat folosindu-ne de formula (a+b)^2 = a^2 + 2ab + b^2

[tex] x^{2} = ( \sqrt{3- \sqrt{5} } )^{2} + 2 \sqrt{(3- \sqrt{5} )(3+ \sqrt{5} )}+( \sqrt{3+ \sqrt{5} } )^{2}\\ x^{2}=3- \sqrt{5}+3+ \sqrt{5}+2 \sqrt{3^{2}- \sqrt{5}^{2} } \\ x^{2}=6+2 \sqrt{4}=6+4=10[/tex]

Care este chiar suprafata patratului x * x

Answer 2

formula radicalilor compusi
√(3-√5)=√[3+√(9-5)]/2-√[3-√(9-5)]/2=√(3+2)/2-√(3-2)/2=√(5/2)-√(1/2)
√(3+√5)=√[3+√(9-5)]/2+√[3-√(9-5)]/2=√(3+2)/2+√(3-2)/2=√(5/2)+√(1/2)

x=√(3-√5)+√(3+√5)=√(5/2)-√(1/2)+√(5/2)+√(1/2)=2√(5/2)

Apatrat=2√(5/2) ×2√(5/2)=4×5/2=10