Question

giải phương trình x(x+2)(x+4)(x+6)=x^4-16

Answer 1

x(x + 2)(x + 4)(x + 6) = x⁴ - 16

=> x(x + 2)(x + 4)(x + 6) = (x² + 4)(x² - 4)

=> x(x + 2)(x + 4)(x + 6) = (x² + 4)(x + 2)(x - 2)

=> (x + 2). [ x(x + 4)(x + 6) - (x² + 4)(x - 2) ] = 0

=> (x + 2). (x³ + 10x² + 24x - x³ + 2x² - 4x + 8) = 0

=> (x + 2) . (12x² + 20x + 8) = 0

=> (x + 2)(x + 1)(3x + 2) = 0

=> x + 2 = 0 => x = -2

hoặc x + 1 = 0 => x = -1

hoặc 3x + 2 = 0 => x = -2/3

Vậy x = {-2 ; -1 ; -2/3}

Answer 2

x(x + 2)(x + 4)(x + 6) = x 4 - 16

=> x(x + 2)(x + 4)(x + 6) = (x 2 + 4)(x 2 - 4)

=> x(x + 2)(x + 4)(x + 6) = (x 2 + 4)(x + 2)(x - 2)

=> (x + 2). [ x(x + 4)(x + 6) - (x 2 + 4)(x - 2) ] = 0

=> (x + 2). (x 3 + 10x 2 + 24x - x 3 + 2x 2 - 4x + 8) = 0

=> (x + 2) . (12x 2 + 20x + 8) = 0 => (x + 2)(x + 1)(3x + 2) = 0

=> x + 2 = 0 => x = -2

hoặc x + 1 = 0 => x = -1

hoặc 3x + 2 = 0 => x = -2/3

Vậy x = {-2 ; -1 ; -2/3}