Question

rozwiąża równania;

a) x^3+x^2-x-1=0

b) 2x^5-5x^4-3x^3=0

c) x+2/x-4=2x-1/x-4

Answer 1

a) x³+x²-x-1=0

x²(x + 1)-(x + 1) = 0

(x + 1)(x² - 1) = 0

(x + 1)(x - 1)( x + 1) = 0

(x + 1)²(x -1) = 0

 

x + 1= 0  ∨  x - 1 = 0

x = -1 ∨ x = 1

x∈{-1,1}

b) 2x⁵-5x⁴-3x³=0

2x⁵-x⁴ - 4x⁴ -3x³=0

(2x⁵ - 4x⁴) + (-x⁴ - 3x³) = 0

2x⁴(x - 2) - x³(x + 3) = 0

(x -2)(x + 3)(2x⁴ - x³) = 0

 

x - 2 = 0 ∨ x + 3 = 0  ∨  2x⁴ - x³ = 0

x = 2  ∨   x = - 3   ∨ x = 0

x∈{2,-3}

c) x+2/x-4=2x-1/x-4

x+2/x-4 -  2x-1/x-4  = 0

-x + 3/x - 4 = 0