cho a/b=c/d CMR a^3/c^3=[2a-b]^3-b^3/[2c-d]^3+d^3 27/08/2021 Bởi Allison cho a/b=c/d CMR a^3/c^3=[2a-b]^3-b^3/[2c-d]^3+d^3
Giải thích các bước giải: $\dfrac{a}{b}=\dfrac{c}{d}$ $\rightarrow \dfrac{a}{c}=\dfrac{b}{d}$ $\rightarrow \dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a}{2c}=\dfrac{b}{d}=\dfrac{2a-b}{2c-d}$ $\rightarrow \dfrac{a^3}{c^3}=\dfrac{b^3}{d^3}=\dfrac{(2a-b)^3}{(2c-d)^3}$ $\rightarrow \dfrac{a^3}{c^3}=\dfrac{(2a-b)^3+b^3}{(2c-d)^3+d^3}\rightarrow đpcm$ Bình luận
Giải thích các bước giải:
$\dfrac{a}{b}=\dfrac{c}{d}$
$\rightarrow \dfrac{a}{c}=\dfrac{b}{d}$
$\rightarrow \dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a}{2c}=\dfrac{b}{d}=\dfrac{2a-b}{2c-d}$
$\rightarrow \dfrac{a^3}{c^3}=\dfrac{b^3}{d^3}=\dfrac{(2a-b)^3}{(2c-d)^3}$
$\rightarrow \dfrac{a^3}{c^3}=\dfrac{(2a-b)^3+b^3}{(2c-d)^3+d^3}\rightarrow đpcm$