Question

Aratati ca (x-1)(x-2)(x-3) = (x-2)^3 (la puterea a treia) -14-x

Answer 1

(x²-2x-x+2)(x-3)= (x-2)(x-2)² -14 -x

(x²-3x+2)(x-3)=(x-2)(x²-4x+4) -14 -x

(x³-3x²+2x-3x²+9x-6)= (x³-4x²+4x-2x²+8x-8)-14 -x

x³-6x²+11x-6=x³-6x²+12x-8-14-x

x³-6x² +11x -6≠x³-6x² +11x-22

egalitatea nu este posibila in conditiile date

Answer 2

$(x-1)(x^2-3x-2x+6)=x^3-6x^2+12x-8-14-x$


Am folosit formula:  $(a-b)^3=a^3-3a^2b+3ab^2-b^3$

$x^3-5x^2+6x-x^2+5x-6=x^3-6x^2-11x-22$

$x^3-6x^2+11x-6=x^3-6x^2-11x-22$

DECI EGALITATEA DATA NU ESTE ADEVARATA!!

(daca ai scris corect enuntul!)