Question

2. Rozwiąż nierówność

a) x^{2} - x-2 \leq 0

b) 3x^{3} > 8x+3

Answer 1

a)

x^2 - x - 2 > 0

 

a = 1 > 0

delta = b^2 - 4ac = ( -1)^2 - 4*1*(-2) = 1 + 8 = 9

p ( delty ) = 3

x1 = [ - b - p(delty) ]/(2a) = [ 1 - 3 ]/2 = -2/2 = - 1

x2 = [ - b + p(delty)]/(2a) = [ 1 + 3]/2 = 4/2 = 2

Odp. ( - oo; - 1) u ( 2; + oo )

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 x^2 - x - 2 <= 0

Odp.

< - 1; 2 >

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b) Po uzgodnieniu treści pytania

  3 x^2 > 8 x + 3

 3 x^2 - 8 x - 3 > 0

delta = ( -8)^2 - 4*3*(-3) = 64 + 36 = 100

p ( delty) = 10

x1 = [ 8 - 10 ]/6 = - 2/6 = - 1/3

x2 = [ 8 + 10]/6 = 18/6 =3

a = 3 > 0

zatem

Odp.

( - oo; - 1/3 ) u ( 3 ; + oo )

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