Question

Daca x+1 pe x = 6 atunci calculati x- 1 pe x

Answer 1

x+1/x=6

(x²+1)/x=6

x²+1=6x

x²-6x+1=0

Δ=36-4=32

x1=(6-4√2)/2=2(3-2√2)/2=3-2√2

x2=3+2√2

S={3-2√2, 3+2√2)

daca x=3-2√2

x-1/x=3-2√2-1/(3-2√2)=3-2√2-(3+2√2)/(9-8)=

=3-2√2-3-2√2=-4√2

daca x=3+2√2

x-1/x=3+2√2-1/(3+2√2)=3+2√2-(3-2√2)/9-8)=

=3+2√2-3+2√2=4√2