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ESERCIZI MATEMATICA (Pag. 391 n°163 ([(x-1)² - (x+1)²]² ≤ (8x+1)(2x-3),…
ESERCIZI MATEMATICA
Pag. 391 n°163
[(x-1)² - (x+1)²]² ≤ (8x+1)(2x-3)
[x²+1-2x-x²-1-2x)]² ≤ 16x²-24x+2x-3
[-4x]² ≤ 16x²-24x+2x-3
16x² ≤ 16x²-24x+2x-3
24x-2x+3 ≤ 0
22x+3 ≤ 0
22x ≤ -3
RISULTATO: x ≤ -3
.
Pag. 391 n°170
x+3 + x+2 + (x-1)² ≥ (x-2)(x+2)
x+3 + x+2 + x²+1-2x ≥ x²-4
2x+6+3x+6+6x²+6-12x ≥ 6x²-24
2x+6+3x+6+6x²+6-12x-6x²+24 ≥ 0
2x+6+3x+6+6-12x+24 ≥ 0
-7x+42 ≥ 0
7x ≤ 42
x ≤ 6
Pag. 565 N.41
3
3
3(2x+2)(3x+3)
3(6x²+12x+6) - 2(6x²+12x+6) > 0
18x²+36x+18-12x²-24x-12 > 0
6x²+12x+6 > 0
Non riuscita
Pag. 391 N. 171
x² - (x+1)² ≥ x-1 - x+1
x²-x²-1-2x ≥ x-1 - x+1
4x²-4x²-4-8x ≥ 2x-2-x-1
4x²-4x²-4-8x-2x+2+x+1 ≥ 0
-9x ≥ -1
x ≥ -1/9
Pag. 565 N. 35
1 ≤ 1
1 ≥ -1
1 +1 ≥ 0
1+2x-1 ≥ 0
2x ≥ 0
Pag. 565 n°34
1
1
1-1(x+3)
-x-2
² ³ ⁴ ⁵ ⁶ ⁷
⁸ ⁹ ≥ ≤
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＿＿
＿＿
３
２
3
＿＿
＿＿
２
＿＿＿＿＿＿＿＿＿＿
６
＿＿＿
６
＿
７
＿
７
＿＿ ＿
22
22
＿
22
＿＿
＿＿
２
4
x+3
＿＿
<
1
＿＿
x+3
-1 < 0
＿＿＿＿
x+3
＿＿
＿＿
２
4
< 0
4
＿＿＿＿＿
＿＿＿＿
4
＿＿
x+3
< 0
N=0 -x-2=0 ---> x=-2
D=0 x+3=0 ---> x=3
RISULTATO: 3>x>-2
m=-1
m=1
＿
9
9
＿
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿
N
D
＿＿
2x-1
-
＿＿
2x-1
＿＿
2x-1
＿＿＿
2x-1
＿＿
2x-1
N=0 2x=0 x=0 m=+
D=0 2x-1=0 x=1/2 m=+
N
D
-2
3
＿＿＿＿＿＿＿＿＿＿＿＿＿
＿＿＿＿＿＿＿＿＿＿＿＿＿
+
+
+
-
-
-
+
-
+
x ≤ 0 V x > 1/2
+
-
-
+
-
-
-
-
+
＿＿ >
＿＿
2x+2
3x+3
2
＿＿ -
2
2x+2
＿＿ > 0
3x+3
＿＿＿＿＿＿＿ -
(2x+2)(3x+3)
2(2x+2)(3x+3)
＿＿＿＿＿＿＿ > 0
(2x+2)(3x+3)
