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Exercitiu rezolvat algebra clasa a 9 a

log ½ (x 2 + 2x) > 0

log ½ (x 2 + 2x) > log ½ 1


(x 2 + 2x) > 0 => x € (-∞, 2) U (0, +∞)
(x 2 + 2x) > 1

(x 2 + 2x) > 0  (conform ecuatiei de gradul doi in care Δ = b 2 - 4ac )
Δ = 4 – 4 * 1 * 0
Δ = 4

x 1 = (-2 + 2) / 2 = 0

x 2 = (- 2 – 2) / 2 = -2

x € (-∞, -2) U (0, +∞)


x
-∞
-2
0
+∞
f(x)
++++++++++++
+++++0---------
---------0+++++
++++++++++++


x 2 + 2x > 1

x 2 + 2x - 1 > 0

Δ = 4 – 4 * 1 (-1)
Δ = 4 + 4
Δ = 8

√Δ = √8
√Δ = √4*2
√Δ = 2√2


=>
x 1 = (-2 + 2√2) / 2 = 2 (-1 + √2)/2     /:2   => x 1 = -1 +√2

x 2 = (-2 - 2√2) / 2 = 2 (-1 - √2)/2      /:2   => x 2 = -1 -√2


x
-∞
-1 -√2
-1 +√2
+∞
f(x)
++++++++++++
+++++0---------
---------0+++++
++++++++++++



x € (-∞,-1 -√2) U (-1 +√2, +∞)



Exercitii rezolvate clasa a 9 a

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