Question

aflati valoarea raportului algebric x la patrat -y la patrat supra lui xy ,pentru x=1-radica din 3 ,y =1+radical din 3

Answer 1

x=1-√3
y=1+√3
(x²-y²)/xy=[(1-√3)²-(1+√3)²]/[(1-√3)(1+√3)]=
=[(1-2√3+3)-(1+2√3+3)]/(1-3)=
=[(4-2√3)-(4+2√3)]/(-2)=
=(4-2√3-4-2√3)/(-2)=0/(-2)=0

Obs: (1-√3)²=1-2√3+√3²=1-2√3+3=4-2√3
folosim regula prescurtata (a-b)²=a²-2ab+b²
(1+√3)²=1+2√3+√3²=1+2√3+3=4+2√3

Answer 2

$\frac{ (1- \sqrt{3}) ^{2}-(1+ \sqrt{3})^{2} }{(1- \sqrt{3})(1+ \sqrt{3}) }= \frac{(1- \sqrt{3}-1- \sqrt{3})(1- \sqrt{3}+1+ \sqrt{3}) }{1-3}= \frac{(-2 \sqrt{3})2 }{-2}=2 \sqrt{3}$