Question

Cho a,b,c\(\in\)_{^{R thỏa mãn \(b^2\)=a.c}}

_{^{Chứng minh \(\frac{a}{c}=\left(\frac{a+2012b}{b+2012c}\right)^2\)}}

giải chi tiết giúp mình nhanh nhanh nha

Answer 1

\(b^2=ac\)

\(\Rightarrow\frac{a}{b}=\frac{b}{c}\)

Đặt \(\frac{a}{b}=\frac{b}{c}=k\), ta có: \(a=bk;b=ck\)

\(\frac{a}{c}=\frac{bk}{c}=\frac{ck\times k}{c}=k^2\) (1)

\(\left(\frac{a+2012b}{b+2012c}\right)^2=\left(\frac{bk+2012b}{ck+2012}\right)^2=\left(\frac{b\left(k+2012\right)}{c\left(k+2012\right)}\right)^2=\left(\frac{b}{c}\right)^2=k^2\) (2)

Từ (1) và (2)

=> \(\frac{a}{c}=\left(\frac{a+2012b}{b+2012c}\right)^2\left(\text{đ}pcm\right)\)

 

Answer 2

mk cũng đang cần. thanks