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\(\frac{\overline{ab}}{\overline{bc}}=\frac{b}{c}=\frac{10a+b}{10b+c}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\frac{\overline{ab}}{\overline{bc}}=\frac{b}{c}=\frac{10a+b}{10b+c}=\frac{10a+b-b}{10b+c-c}=\frac{10a}{10b}=\frac{a}{b}\)
\(\Rightarrow\frac{b}{c}=\frac{a}{b}\Rightarrow b^2=ac\)
\(\frac{a^2+b^2}{b^2+c^2}=\frac{a^2+ac}{ac+c^2}=\frac{a\left(a+c\right)}{c\left(a+c\right)}=\frac{a}{c}\)
\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
\(\Rightarrow\left(a^2+b^2\right)cd=ab\left(c^2+d^2\right)\)
\(\Leftrightarrow a^2cd+b^2cd=abc^2+abd^2\)
\(\Leftrightarrow ac\left(ad-bc\right)-bd\left(ad-bc\right)=0\)
\(\Leftrightarrow\left(ac-bd\right)\left(ad-bc\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}ac=bd\\ad=bc\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{a}{b}=\frac{d}{c}\\\frac{a}{b}=\frac{c}{d}\end{cases}}\).
Ta có : \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
\(\Leftrightarrow\left(a^2+b^2\right)cd=ab\left(c^2+d^2\right)\)
\(\Leftrightarrow a^2cd+b^2cd=abc^2+abd^2\)
\(\Leftrightarrow\left(a^2cd-abd^2\right)+\left(b^2cd-abc^2\right)=0\)
\(\Leftrightarrow ad\left(ac-bd\right)-bc\left(ac-bd\right)=0\)
\(\Leftrightarrow\left(ac-bd\right)\left(ad-bc\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}ac=bd\\ad=bc\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{a}{b}=\frac{c}{d}\\\frac{a}{b}=\frac{d}{c}\end{cases}}\) (đpcm)
\(\frac{\overline{ab}}{a+b}=\frac{\overline{bc}}{b+c}\) hay \(\frac{10a+b}{a+b}=\frac{10b+c}{b+c}\)
\(\left(10a+b\right)\left(b+c\right)=\left(a+b\right)\left(10b+c\right)\)
\(10ab+b^2+10ac+bc=10ab+10b^2+ac+bc\)
\(9ac=9b^2\)
\(ac=b^2\)
\(\frac{a}{b}=\frac{b}{c}\)
\(\frac{10a+b}{a+b}=\frac{10b+c}{b+c}\)=\(1+\frac{9a}{a+b}=1+\frac{9b}{b+c}\)
\(\frac{9a}{a+b}=\frac{9b}{b+c}=>\frac{9a}{9b}=\frac{a+b}{b+c}\)
\(\frac{a}{b}=\frac{a+b}{b+c}=\frac{a+b-a}{b+c-b}=\frac{b}{c}\)
=>\(\frac{a}{b}=\frac{b}{c}\)
nếu đúng thì k nka
Đặt \(\frac{a}{b}=\frac{c}{d}=k\) ,ta có:
\(a=bk,c=dk\)
\(\Rightarrow\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{\left(bk+b\right)^2}{\left(dk+d\right)^2}=\frac{\left[b.\left(k+1\right)\right]^2}{\left[d.\left(k+1\right)\right]^2}=\frac{b^2.\left(k+1\right)^2}{d^2.\left(k+1\right)^2}=\frac{b^2}{d^2}\)(1)
\(\frac{ab}{cd}=\frac{bkb}{dkd}=\frac{b^2}{d^2}\)(2)
Từ (1) và (2) suy ra:
\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{ab}{cd}\)(đpcm)
b2-c2=(a2+b2)-(a2-c2)/c
a2+b2/a2+c2-1=b/c-1
a2+b2-(a2+c2)/a2+c2=b-c/c
=b2-c2/a2+c2=b-c/c(ĐPCM)
Làm đầu tiên nhé