CHo $\dfrac{a}{b}$ = $\dfrac{c}{d}$ CMR: $\dfrac{(a-b)^2}{(c-d)^2}$ = $\dfrac{ab}{cd}$ 03/12/2021 Bởi Sarah CHo $\dfrac{a}{b}$ = $\dfrac{c}{d}$ CMR: $\dfrac{(a-b)^2}{(c-d)^2}$ = $\dfrac{ab}{cd}$
Đặt `a/b=c/d=k` $⇒a=b.k,\ c=d.k$ Ta có: `VT=(a-b)^2/(c-d)^2=(bk-b)^2/(dk-d)^2=[b(k-1)^2]/[d(k-1)]^2=b^2/d^2` `VP=(ab)/(cd)=(bk.b)/(dk.d)=b^2/d^2` $⇒VT=VP$ Vậy `(a-b)^2/(c-d)^2=(ab)/(cd)`. Bình luận
Giải thích các bước giải:
Đặt `a/b=c/d=k`
$⇒a=b.k,\ c=d.k$
Ta có: `VT=(a-b)^2/(c-d)^2=(bk-b)^2/(dk-d)^2=[b(k-1)^2]/[d(k-1)]^2=b^2/d^2`
`VP=(ab)/(cd)=(bk.b)/(dk.d)=b^2/d^2`
$⇒VT=VP$
Vậy `(a-b)^2/(c-d)^2=(ab)/(cd)`.