Question

Stiind ca x+y+z=6 ,calculeaza:
a) x,(y) barat +y,(z)barat+z,(x)=
b)x,y(z) barat+y,z(x) barat+z,x(y)barat =
Va rog repede !!
Dau coroana

Answer 1

[tex]a)\overline{x,(y)}+\overline{y,(z)}+\overline{z,(x)}=x\dfrac{y}{9}+y\dfrac{z}{9}+z\dfrac{x}{9}=\dfrac{9x+y}{9}+\dfrac{9y+z}{9}+\dfrac{9z+x}{9}\\ =\dfrac{10x+10y+10z}{9}=\dfrac{10(x+y+z)}{9}=\dfrac{60}{9}=\dfrac{20}{3}\\ \\ b)\overline{x,y(z)}+\overline{y,z(x)}+\overline{z,x(y)}=x\dfrac{\overline{yz}-y}{90}+y\dfrac{\overline{zx}-z}{90}+z\dfrac{\overline{xy}-x}{90}=\\ =\dfrac{90x+10y+z-y}{90}+\dfrac{90y+10z+x-z}{90}+\dfrac{90z+10x+y-x}{90}}=\\ =\dfrac{100x+100y+100z}{90}=\dfrac{100(x+y+z)}{90}=\dfrac{60}{9}=\dfrac{20}{3}[/tex]