dane:
x+y+z=126
x*y*z= 13824
y²=xz / srodkowy jest sred. geom skrajnych
y³= 13824----->y=24
x+z=102---->z=102-x
xz=576
102x-x²=576
x²-102x+576=0
Δ=10404-2304=8100
√Δ=90
x1=(102-90)/2=6---->z1=96
x2=96----->z2=6
0dp 6,24,96 lub 96,24,6
Zad 2
Dane: a1,a2,a3 - ciag arytm ------>a2=(a1+a3)/2
(a1-8),a2,a3 ---ciag geom ------->(a2)²=(a1-8)*a3
a1+a2+a3=26+8
a1+a3=2a2
z (3)-------> 3a2=34------>a2=34/3=11,33
a1+a3=68/3----------->a3=68/3-a1
(a1-8)*a3 =(34/3)²
(a1-8)*(68/3-a1) =(34/3)²
68/3a1-a1²-544/3+8a1=1156/9 mnoze przez 9
204a1-9a1²-1632+72a1=1156
9a1²-276a1-476=0
Δ=76176+36*476=76176+17136=93312
√Δ=305,470
a11=(276-305,470)/18=-1,6372----->a31=68/3-a1=24,30
a12=(276+305,470)/18=32,3--------->a32=68/3-a1=-9,63
odp: trzeba jeszcze raz sprawdzic.
-1,6372 ; 11,33 ; 24,30
lub
32,3 ; 11,33 ; -9,63
