Question

1) Cho a/b = b/c = c/d = d/a ( với a,b,c,d khác 0 . Tính giá trị biểu thức :

M = (a+b)/(c+d) + (b+c)/(d+a) +(c+d)/(a+b)+(d+a)/(d+c)

2) Cho a/b = c/d. Chứng minh rằng :

7a^2 + 3ab/11a^2 - 8b^2 = 7c^2 + 3cd/11c^2 - 8d^2

Answer 1

Câu 2: 

Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2k^2+3bk\cdot b}{11\cdot b^2k^2-8b^2}=\dfrac{7b^2k^2+3b^2k}{11b^2k^2-8b^2}=\dfrac{7k^2+3k}{11k^2-8}\)

\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7\cdot d^2k^2+3\cdot dk\cdot d}{11\cdot d^2k^2-8d^2}=\dfrac{7k^2+3k}{11k^2-8}\)

Do đó: \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)