Question

Daca x si a sunt numere rationale pozitive inverse , y si b sunt numere rationale pozitive inverse si x ori y = 2 supra 3 , calculeaza a ori b

Answer 1

a si x, inverse,⇒ax=1
b si y, inverse⇒by=1
xy=2/3

abxy=ax*by=1
ab*(xy)=1
ab*(2/3)=1
ab=1*3/2
ab=3/2
as simple as that!!!

Answer 2

[tex]\it a,\ x \in\mathbb{Q}_+; \ \ a,\ \ x\ sunt\ inverse\ \Rightarrow a = \dfrac{1}{x}\ \ \ \ (1) \\\;\\ b,\ y \in\mathbb{Q}_+; \ \ b,\ \ y\ sunt\ inverse\ \Rightarrow b = \dfrac{1}{y}\ \ \ \ (2) \\\;\\ x\cdot y= \dfrac{2}{3}\ \ \ \ \ (3)[/tex]

$\it \ (1),\ (2) \ \Rightarrow a\cdot b =\dfrac{1}{x}\cdot\dfrac{1}{y} =\dfrac{1}{x\cdot y} = \dfrac{1}{\dfrac{2}{3}} =1:\dfrac{2}{3} =1\cdot\dfrac{3}{2}=\dfrac{3}{2}$