Question

3x^2+2x-5≤x^2+x+1
RESUELVE ESTA INECUACION

Answer 1

Explicación paso a paso:

3x2 + 2x - 5 ≤ x2 + x + 1 | ‑ x2 ‑ x ‑ 1

2x2 + x - 6 ≤ 0

2x2 + x ‑ 6 = 0

D = b2 - 4 * a * c

a = 2 b = 1 c = ‑ 6

D = (1)2 - 4 * 2 * (‑ 6) = 1 + 48 = 49

D > 0 => x1,2 = -b ± √D

_____

2 * a

x1,2 = ‑ 1 ± √49 ‑ 1± 7

______ = ______

2 * 2 4

X1 = - 1 -7 -8

___ = ___ = - 2

4 4

X2 = - 1 + 7 6 3

_____ = _____ = ___ (x2 = 1.5)

4 4 2

2x2 + x - 6 ≤ 0

solución :

‑ 2 ≤ x ≤ 3

___

2

[‑ 2, 3

__ ]

2