Question

X+1/x=6 , aflati x-1/x.

Answer 1

x+1/x=6 =>

x²+1=6x

x²-6x+1=0

Δ=36-4=32

x1=(6+√32)/2=(6+4√2)/2=3+2√2

x2=(6-√32)/2=...-3-2√2

Observi ca x*1/x=1

adica (3+2√2)*(3-2√2)=9-8=1

Decix1=1/x2   si     x2=1/x1

x-1/x1=3+√2-(3-√2)=2√2

x2-1/x2=3-√2-(3+2√2)=3-√2-3-2√2=-3√2