Question

Chứng minh rằng : Nếu \(\frac{a+b}{b+c}=\frac{c+d}{d+a}\) thì a = choặc a + b + c + d = 0

Answer 1

a=?

Answer 2

\(\frac{a+b}{b+c}=\frac{c+d}{d+a}\Rightarrow\left(a+b\right)\left(d+a\right)=\left(c+d\right)\left(b+c\right)\)

=> a²+ab+ad+db=cb+c²+db+dc

=> a²+ab+ad+db-cb-c²-db-dc=0

=>( a²-c²) + (ab -bc) +( ad -dc)=0

=>(a+c)(a-c) +b(a-c) +d(a-c)=0

=>(a-c)(a+c+b+d)=0

=>\(\left[\begin{array}{nghiempt}a-c=0\\a+b+c+d=0\end{array}\right.\)

=>\(\left[\begin{array}{nghiempt}a=c\\a+b+c+d=0\end{array}\right.\)

Answer 3

đề như đệt