Question

daca x + 1/x =7 calculați x-1/x

Answer 1

 x + 1/x =7, x diferit de zero

x^2 +1=7x, ''^''=la puterea

x^2 -7x+1=0

D=49-4=45, VD=V45=3V5, ''D''=delta, ''V''=radical

x1;2=(7+/-VD)/2=(7+/-3V5)/2

x1=(7-3V5)/2

x2=(7+3V5)/2


x1-1/x1=(7-3V5)/2 -2/(7-3V5)=

=(7-3V5)/2 -2(7+3V5)/(49-45)=

=(7-3V5)/2 -(7+3V5)/2=(-6V5)/2=-3V5


x2-1/x2=(7+3V5)/2 -2/(7+3V5)=

(7+3V5)/2 -2(7-3V5)/4=

(7+3V5)/2 -(7-3V5)/2=

=(+6V5)/2=3V5