Question

Exercitiile 23,24....

Answer 1

23.

mx2-x-1-m=<0 pt orice x real

inecuatia este indeplinita daca intervalul [x1,x2] tinde catre 0, unde x1,2 sunt solutiile ecuatiei mx2-x-1-m=0.

acest interval tinde spre 0 daca x1=x2

Δ=(-1)²+4m(m+1)=1+4m²+4m=(2m)²+2*2m+1=(2m+1)²

x1,2=(-b+-√Δ)/2a

x₁=[1+(2m+1)]/2m=(m+1)/m

x₂=[1-(2m+1)]/2m=(-2m)/2m=-1

x₁=x₂

(m+1)/m=-1

m+1=-m

2m+1=0

m=-1/2