BT 8.4 :
a,Ta có: \(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{ab}{cd}\) = k
\(\Rightarrow a=bk;c=dk\)
Thay a = bk; c = dk vào VT ta được:
\(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{\left(bk\right)^2-b^2}{\left(dk\right)^2-d^2}=\dfrac{b^2\left(k^2-1\right)}{d^2\left(k^2-1\right)}=\dfrac{b^2}{d^2}\)
Thay a = bk; c = dk vào VP ta được:
\(\dfrac{ab}{cd}=\dfrac{bk\times b}{dk\times d}=\dfrac{b^2}{d^2}\)
\(\Rightarrow\) VT = VP
Vậy \(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{ab}{cd}\)
b,Ta có \(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{ab}{cd}=k\)
\(\Rightarrow a=bk;c=dk\)
Thay a = bk; c = dk vào VT ta được:
\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{\left(bk-b\right)^2}{\left(dk-d\right)^2}=\dfrac{\left[b\times\left(k-1\right)\right]^2}{\left[d\times\left(k-1\right)\right]^2}=\dfrac{b^2}{d^2}\)
Thay a = bk; c = dk vào VP ta được:
\(\dfrac{ab}{cd}=\dfrac{bk\times b}{dk\times d}=\dfrac{b^2}{d^2}\) \(\Rightarrow\)
VT = VP Vậy \(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{ab}{cd}\) xl bn nk tui chưa làm đc bài 8.6*
\(\dfrac{ab}{cd}=\dfrac{bk\times b}{dk\times d}=\dfrac{b^2}{d^2}\)
