1) 2х²+7х-4<0
график парабола, ветви вверх
2х²+7х-4=0
D = 49 + 32 = 81 = 9²
x(1) = (-7+9) / 4 = 1/2
x(2) = (-7-9) / 4 = -4
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-------o-------o------->x
-4 1/2
х∈(-4; 1/2)
2)3х²-5х-2>0
график парабола, ветви вверх
3х²-5х-2=0
Д = 25+24 = 49 = 7²
х(1) = (5+7)/6 = 2
х(2) = (5-7) /6 = -1/3
/////// ////////
-------о---------о------->x
-1/3 2
x∈(-∞; -1/3)∪(2; +∞)
3)-2х²+х1≥0
график парабола, ветви вниз
-2x²+x+1=0
D = 1+8 = 9 = 3²
x(1) = (-1+3) / -4 = -2/4=-1/2
x(2) = (-1-3) / -4 = -4/-4 = 1
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------*-------*------>x
-1/2 1
x∈[-1/2; 1]
4)-4х²+3х+1≤0
график парабола , ветви вниз
-4x²+3x+1 = 0
D = 9+16 = 25 = 5²
x(1) = (-3+5)/-8 = -1/4
x(2) = (-3-5) / -8 = 1
//////// /////////
--------*-------*------->x
-1 -1/4
x∈(-∞; -1]∪[-1/4; +∞)
9(4 - x)^2 - 16 = (3(4 - x) - 4) (3(4 - x) + 4) =
= (12 - 3x - 4) (12 - 3x + 4) =
= (8 - 3x) ( 16 - 3x) =
= (3x - 8) (3x - 16)
б)
a^2 - b^2 = (a - b)( a + b)
(x + 2 - 5)( x + 2 + 5) = 0
(x - 3) (x + 7) = 0
x = 3;
x = - 7