Tham khảo: https://hoc247.net/hoi-dap/toan-7/chung-minh-a-2-c-2-b-2-c-2-a-b-biet-a-c-c-d-faq430384.html

Đề chưa đủ.

tham khảo tại link nek:

https://h.vn/hoi-dap/question/500717.html

~ho ktoost~

a)

Ta có

\(\frac{a}{c}=\frac{c}{b}\Rightarrow\frac{a^2}{c^2}=\frac{c^2}{b^2}=\frac{a^2+c^2}{c^2+b^2}\)

\(\frac{a}{b}=\frac{a}{c}.\frac{c}{b}=\left(\frac{a}{c}\right)^2\)

Mà\(\frac{a^2+c^2}{b^2+c^2}=\left(\frac{a}{c}\right)^2=\frac{a}{b}\). Vậy \(\frac{a^2+c^2}{b^2+c^2}=\frac{a}{b}\)

câu b đâu

mk thì trả hiểu cậu làm ntn ???

A. Ta có : a^2 (b+c)= b^2(a+c)

→ a^2(b+c)- b^2(a+c) =0

→ aab+aac-bba-bbc =0

→ (aab-bba) + ( aac-bbc) =0

→ ab (a-b )+ c(a+b)(a-b) =0

→[ c(a+b)+ab] . (a-b) =0

Mà a-b khác 0

→ c(a+b) +ab =0

→ac+bc+ab=0

→ b(a+c)=-ac

→ b^2 (a+c) =-abc

Mà b^2 (a+c) =2015 ( đề bài )

→ -abc =2015

→ ĐPCM

a^2*(b+c)=b^2*(a+c)=>2015/a^2-b=2015/b^2-a

2015/b^2-2015/a^2=a-b

2015*a^2-2015*b^2=(a-b)*a^2*b^2

2015*a^2-2015*b^2=a*b^2*a^2-a^2*b*b^2

=>a*b^2=2015;a^2*b=2015

=>a*b^2=a^2*b

=>b^2=a*b;a^2=a*b

=>a^2=b^2

=>a=b hoặc a=-b.Mà a,b,c đôi một khác nhau

=>a=-b=>a+b=0=>A=c^2*(a+b)=0

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\left(\frac{a}{c}\right)^2=\left(\frac{b}{d}\right)^2\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}\)
\(\Rightarrow\hept{\begin{cases}\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a^2+b^2}{c^2+d^2}\\\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a^2-b^2}{c^2-d^2}\end{cases}}\)
\(\Rightarrow\frac{a^2+b^2}{c^2+d^2}=\frac{a^2-b^2}{c^2-d^2}\)
\(\Rightarrow\frac{a^2+b^2}{a^2-b^2}=\frac{c^2+d^2}{c^2-d^2}\)
Vậy ​​\(\frac{a^2+b^2}{a^2-b^2}=\frac{c^2+d^2}{c^2-d^2}\)