Question

Rezolvati: (x+3)^3-25x-75=(x-2)(x+8)(x+3)

Answer 1

x³+9x²+27x+27-25x-75=(x-2)(x²+3x+8x+24)
x³+9x²+2x-48=(x-2)(x²+11x+24)
x³+9x²+2x-48=x³+11x²+24x-2x²-22x-48
x³+9x²+2x-48=x³+9x²+2x-48
x³+9x²+2x-48-x³-9x²-2x+48=0
nu are solutii x∈Ф

Answer 2

(x+3)³ -25x-75= (x-2)(x+8)(x+3) 
x³+9x²+ 27x+ 27-25x- 75  = ( x²+8x-2x-16)(x+3)
x³+9x²+2x-48= (x²+6x-16)(x+3)
x³+9x²+2x-48= x³ +3x²+6x²+18x-16x-48
x³-x³+9x²-9x²+2x-18x= 0
-16x= 0⇒ x=0