Question

[Khánh Vinh]

1.a)\(Cho\frac{a}{b}=\frac{b}{c}=\frac{c}{d}.\)Chứng minh rằng:\(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)

b) Tìm giá trị biểu thức A, biết A=\(\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}(a,b,c\ne0)\)

Answer 1

[Xyz OLM]

Ta có \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}\)

=> \(\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b+c}{b+c+d}\right)^3\)

=> \(\left(\frac{a}{b}\right)^3=\left(\frac{a+b+c}{b+c+d}\right)^3\)

=> \(\frac{a}{b}.\frac{a}{b}.\frac{a}{b}=\left(\frac{a+b+c}{b+c+d}\right)^3\)

=> \(\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\) (Vì \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\))

=> \(\frac{a}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\)(đpcm)