Question

Relatia X₁*X₂=c/a,este valabila pentru ecuatia ax²+bx+c=0,a≠0,cu solutiile reale X₁ si X₂. Calculati : X₂ pentru ecuatia :

a) X²-5X+4=0,daca X₁=4.
b) 3/7X²-2X+11/7=0,daca X₁=1.
c) -X²+14X-24=0,daca X₁=2.
d) 5X²+√3X-12=0,daca X₁= -√3.
Vreau rezolvarea completa !

Answer 1

a) X²-5X+4=0,daca X₁=4.
x₁ × x₂ =4/1
4 × x₂ =4  ⇒ x₂=1

b) 3/7X²-2X+11/7=0,daca X₁=1
x₁ × x₂ =(11/7)/(3/7)
1 × x₂ =11/3  ⇒ x₂=11/3

c) -X²+14X-24=0,daca X₁=2.
x₁ × x₂ =(-24)/(-1)
2 × x₂ =24  ⇒ x₂=12

d) 5X²+√3X-12=0,daca X₁= -√3.
x₁ × x₂ =(-12)/5
-√3 × x₂ =-12/5  ⇒ x₂=(4√3)/5