$\frac{a^{3}}{(a-b)(a-c)}$ + $\frac{b^{3}}{(b-a)(b-c)}$ + $\frac{c^{3}}{(c-a)(c-b)}$ 20/08/2021 Bởi Isabelle $\frac{a^{3}}{(a-b)(a-c)}$ + $\frac{b^{3}}{(b-a)(b-c)}$ + $\frac{c^{3}}{(c-a)(c-b)}$
Đáp án: Giải thích các bước giải: $\dfrac{a^3}{(a-b)(a-c)}+\dfrac{b^3}{(b-a)(b-c)}+\dfrac{c^3}{(c-a)(c-b)}$ $=\dfrac{-a^3}{(a-b)(c-a)}+\dfrac{-b^3}{(a-b)(b-c)}+\dfrac{-c^3}{(c-a)(b-c)}$ $=\dfrac{-a^3(b-c)-b^3(c-a)-c^3(a-b)}{(a-b)(b-c)(c-a)}$ $=\dfrac{-a^3b+a^3c-b^3c+ab^3-ac^3+bc^3}{(a-b)(b-c)(c-a)}$ $=\dfrac{-ab(a^2-b^2)+c(a^3-b^3)-c^3(a-b)}{(a-b)(b-c)(c-a)}$ $=\dfrac{-ab(a-b)(a+b)+c(a-b)(a^2+ab+b^2)-c^3(a-b)}{(a-b)(b-c)(c-a)}$ $=\dfrac{(a-b)(-a^2b-ab^2+a^2c+abc+b^2c-c^3}{(a-b)(b-c)(c-a)}$ $=\dfrac{-a^2(b-c)-ab(b-c)+c(b^2-c^2)}{(b-c)(c-a)}$ $=\dfrac{(b-c)(-a^2-ab+bc+c^2}{(b-c)(c-a)}$ $=\dfrac{(c-a)(c+a)+b(c-a)}{c-a}$ $=\dfrac{(c-a)(c+a+b)}{c-a}$ $=a+b+c$Chúc bạn học tốt !!! Bình luận
Đáp án:
Giải thích các bước giải:
$\dfrac{a^3}{(a-b)(a-c)}+\dfrac{b^3}{(b-a)(b-c)}+\dfrac{c^3}{(c-a)(c-b)}$
$=\dfrac{-a^3}{(a-b)(c-a)}+\dfrac{-b^3}{(a-b)(b-c)}+\dfrac{-c^3}{(c-a)(b-c)}$
$=\dfrac{-a^3(b-c)-b^3(c-a)-c^3(a-b)}{(a-b)(b-c)(c-a)}$
$=\dfrac{-a^3b+a^3c-b^3c+ab^3-ac^3+bc^3}{(a-b)(b-c)(c-a)}$
$=\dfrac{-ab(a^2-b^2)+c(a^3-b^3)-c^3(a-b)}{(a-b)(b-c)(c-a)}$
$=\dfrac{-ab(a-b)(a+b)+c(a-b)(a^2+ab+b^2)-c^3(a-b)}{(a-b)(b-c)(c-a)}$
$=\dfrac{(a-b)(-a^2b-ab^2+a^2c+abc+b^2c-c^3}{(a-b)(b-c)(c-a)}$
$=\dfrac{-a^2(b-c)-ab(b-c)+c(b^2-c^2)}{(b-c)(c-a)}$
$=\dfrac{(b-c)(-a^2-ab+bc+c^2}{(b-c)(c-a)}$
$=\dfrac{(c-a)(c+a)+b(c-a)}{c-a}$
$=\dfrac{(c-a)(c+a+b)}{c-a}$
$=a+b+c$
Chúc bạn học tốt !!!