Question

Rezolvati in R ecutiile si determinati ce tip de numere ,rationale sau irationale sunt solutiile ei:
a)2,5(x-4)-6x egal 3-x
b)-x² + 10x+2 egal 0(zero)

Answer 1

a)2,5 (x-4) -6x = 3-x
2,5x -10- 6x =3-x
-3,5x-10= 3-x
-3,5x +x = 3+10
-2,5x = 13
x= - 5,2 ⇒ x ∈ Q ( rationale)
b)
[tex]-x^2 + 10x +2 = 0 \\ \\ x=\frac{-10 += \sqrt{10^2 - 4*(-1) *2} }{2*(-1)} \\ \\ x= \frac{-10 +- \sqrt{100 + 8} }{-2} \\ \\ x= \frac{-10 +- \sqrt{108} }{-2} \\ \\ x= -\frac{-10 +- 6 \sqrt{3} }{2} \\ \\ x_{1} = - \frac{-10+6 \sqrt{3} }{2} =\ \textgreater \ x_{1}=5-3 \sqrt{3} \\ \\ x_{2} =- \frac{-10-6 \sqrt{3} }{2} =\ \textgreater \ x_{2} = 5 +3 \sqrt{3} [/tex]
$x_{1}$ ∈ I ( irationale)
$x_{2}$ ∈ I ( irationale)