<h3>х² - 2|х| - 15 = 0</h3><h3>( |х| )² - 2|х| - 15 = 0</h3><h3>Пусть |х| = а , а ≥ 0 , тогда</h3><h3>а² - 2а - 15 = 0</h3><h3>D = (-2)² - 4•(-15) = 4 + 60 = 64 = 8²</h3><h3>a₁ = - 3 ⇒ ∅</h3><h3>a₂ = 5 ⇒ |x| = 5 ⇒ x = ± 5</h3><h3><em><u>ОТВЕТ: - 5 ; 5</u></em></h3><h3><em><u /></em></h3>
A) x² - 9 ≤ 0
1) (x - 3)(x + 3) ≤ 0
2) x² ≤ 9
3) 9 - x² ≥ 0
б) 1/x < 1/3
1) 1/x - 1/3 < 0
2) (3-x)/(3x) < 0
3) (x-3)/(3x) > 0
1)log1/16 (14-x)=-2
14-x= (1/16)ˇ-2
14-x=16²
14-x=256
x=14-256, x= -242
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2)(1/3)ˇ(x+11)=1/81
(1/3)ˇ(x+11)=(1/3)ˇ4
x+11=4, x=4-11
x=-7
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5 ^ 45 + 5 ^ 44 - 5 ^ 43 = 5 ^ k * 29
5 ^ 43 * ( 5^2 + 5 - 1 ) = 5 ^ k * 29
5 ^ 43 * 29 = 5 ^ k * 29
5 ^ 43 = 5 ^ k
k = 43
2)
y : 5 ^ 2 = 5
y = 5 ^ 2 * 5
y = 5 ^ 3
y = 125
{7x-3y/5=-4 |·5
{x+2y/5=-3 |·5
{35x-3y=-20
{5x+2y=-15 |·(-7)
{35x-3y=-20
{-35x-14y=105 сложим почленно первое со вторым
-17y=85
y=-5
5x+2·(-5)=-15
5x=-5
x=-1 ответ(-1;-5)