Question

Cho a/b = b/c = c/d = d/a
Tính: P= 2a-b/2c-d + 2b-c/2d-a + 2c-d/2a-b + 2d-a/2b-c

Answer 1

Answer 2

Đặt: \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}=k\)

=> \(\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}.\dfrac{d}{a}=k^4\)

=> k = \(\pm\)1

Với k = 1 thì \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}\Rightarrow a=b=c=d\)

=> P = 4

Với k = -1 thì \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}=-1\) => \(\left\{{}\begin{matrix}a=-b\\b=-c\\c=-d\\d=-a\end{matrix}\right.\) => a = -b = c = -d

=> P = \(\dfrac{2a+a}{2a+a}+\dfrac{-2a-a}{-2a-a}+\dfrac{2a+a}{2a+a}+\dfrac{-2a-a}{-2a-a}=4\)

Vậy P luôn bằng 4.