x+1,1-x si 4 sunt in progresie geometrica daca:
1-x=√4(x+1)
C.E. 1-x≥0⇒x≤1
x+1≥0⇒x≥-1
x∈[-1,1]
Ridicam la patrat egalitatea de mai sus:
(1-x)²=4(x+1)
1-2x+x²-4x-4=0
x²-6x-3=0
Δ=36+12=48
x1/2=(6+/-4√3)/2=3+/-2√3
3+2√3≈6,46
3-2√3≈-0,46
Valoarea buna este x=3-2√3.
Verificare
3-2√3+1=4-2√3=2(2-√3)
1-(3-2√3)=2√3-2=2(√3-1)
4
Ratia √3 +1
