Question

În ce parte se înclină balanță?
Vă rog să îmi faceți calculele complet.

Answer 1

(A) (1/2-1/3)(1/2+1/3 = (1/2)^2-(1/3)^2=1/4-1/9= =(9-4)36= 5/36; A=5/36

(B) (2^-1 +3^-1)^2=(1/2+1/3)^2=1/4+2/6+1/9=
=1/4+1/3+1/9=(9+12+4)/36=25/36 ;

A=5/36 B=25/36

5/36 si 25/36 => 5/36 < 25/36 => A<B
Balanta se va inclina in partea dreapta

Answer 2

$a=\Big(\frac{1}{2}-\frac{1}{3}\Big)\Big(\frac{1}{2}+\frac{1}{3}\Big)$
$b=(2^{-1}+3^{-1})^{2}=$
$\Big(\frac{1}{2}+\frac{1}{3}\Big)\Up^{2}$
$\Big(\frac{1}{2}+\frac{1}{3}\Big)\Big(\frac{1}{2}+\frac{1}{3}\Big)$
$Comparam~a~si~b$
$a~are~un~minus~in~prima~paranteza,~iar~b~are~plus,~deci~b>a$
$Balanta~se~inclina~in~dreapta$