Question

[Khuất Mai Trúc]

Chứng minh rằng: Nếu  \(\frac{a+b}{a-b}=\frac{c+a}{c-a}\) thì a² =bc

Answer 1

[An Hoà]

\(\frac{a+b}{a-b}=\frac{c+a}{c-a}\)

=> ( a + b ) ( c -a ) = ( a - b ) ( c + a )

=> a ( c - a ) + b ( c -a ) = c ( a - b ) + a ( a - b )

=> ac - aa + bc - ab = ac - bc + aa - ab

=> - aa - aa = - bc - bc

=> - 2 . a ²  = - 2 . bc

=> a ² = bc

Vậy \(\frac{a+b}{a-b}=\frac{c+a}{c-a}\)thì a ² = bc