Решить показательные уравнения и неравенства!

Question

Алгебра: Решить показательные уравнения и неравенства!

adamchik · Accepted Answer

N 1
x^2 - 5x = 14
x^2 - 5x - 14 = 0
D = 25 + 56 = 81 = 9^2
x1 = ( 5 + 9 ) : 2 = 7
x2 = ( 5 - 9 ) : 2 = - 2
N 2
9 + 4x^2 - 12x = 0
4x^2 - 12x + 9 = 0
D = 144 - 144 = 0
x = 12 : 8 = 1,5
N 3
2x^2 - 9x - 5 = 0
D = 81 + 40 = 121 = 11^2
x1 = ( 9 + 11 ) : 4 = 5
x2 = ( 9 - 11 ) : 4 = - 0,5
N 4
4x^2 = 9 + 16x
4x^2 - 16x - 9 = 0
D = 256 + 144 = 400 = 20^2
x1 = ( 16 + 20 ) : 8 = 4,5
x2 = ( 16 - 20 ) : 8 = - 0,5
N 5
3 + 4x^2 - x = 0
4x^2 - x + 3 = 0
D = 1 - 48 = - 47
D < 0 ; Нет корней
N 6
x^2 + x = 0
x( x + 1 ) = 0
x1 = 0
x2 = - 1
N 7
8 - 2с^2 = 0
2( 4 - c^2 ) = 0
2( 2 - c )( 2 + c ) = 0
C1 = 2
C2 = - 2

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