1)
x-1/x=a⇒x²+1/x²=a²+2
a²+2-1/2*a=7/2
2a²+4-a-7=0
2a²-a-3=0
D=1+24=25
a1=(1-5)/4=-1⇒x-1/x=-1
x²+x-1=0
D=1+4=5
x1=(-1-√5)/2 U x2=(-1+√5)/2
a2=(1+5)/4=3/2⇒x-1/x=3/2
2x²-3x-1=0
D=9+8=17
x3=(3-√17)/4 U x4=(3+√17)/4
2)
x+1/x=a⇒x²+1/x=a²-2
a²-2-1/3*a=8
3a²-6-a-24=0
3a²-a-30=0
D=1+360=361
a1=(1-19)/6=-3⇒x+1/x=-3
x²+3x+1=0
D=9-4=5
x1=(-3-√5)/2 U x2=(-3+√5)/2
a2=(1+19)/6=10/3⇒x+1/x=10/3
3x²-10x+1=0
D=100-12=88
x3=(10-2√22)/6=(5-√22)/3 U x4=(5+√22)/3