Question

[#Lonely_Darkness#]

1. cho\(\frac{a}{b}\)=\(\frac{c}{d}\)c/m

a)  \(\frac{7a^2+3ab}{11a^2-5b^2}\)=\(\frac{7c^2+3cd}{11c^2-5d^2}\)

b)\(\frac{a^4}{b^4}\)=\(\left(\frac{a+b}{c+d}\right)^4\)=\(\frac{a^4+b^4}{c^4+d^4}\)

c)\(\frac{ac}{bd}\)=\(\left(\frac{a+c}{b+d}\right)^2\)

help me!

Answer 1

[Nguyệt]

a) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{7a^2}{7c^2}=\frac{3b^2}{3d^2}=\frac{3ab}{3cd}=\frac{11a^2}{11c^2}=\frac{5b^2}{5d^2}\)

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{7a^2}{7c^2}=\frac{3b^2}{3d^2}=\frac{3ab}{3cd}=\frac{11a^2}{11c^2}=\frac{5b^2}{5d^2}=\frac{7a^2+3ab}{7b^2+3cd}=\frac{11a^2-5b^2}{11c^2-5d^2}\)

\(\Rightarrow\frac{7a^2+3ab}{11a^2-5b^2}=\frac{7c^2+3cd}{11c^2-5d^2}\)

b) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^4}{c^4}=\frac{b^4}{d^4}\)

áp dụng t.c dãy tỉ số bằng nhau ta có:

\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\Rightarrow\frac{a^4}{c^4}=\frac{b^4}{d^4}=\left(\frac{a+b}{c+d}\right)^4\)(1)

\(\frac{a^4}{c^4}=\frac{b^4}{d^4}=\frac{a^4+b^4}{c^4+d^4}\)(2)

từ (1) và (2) => đpcm

c) áp dụng t.c dãy tỉ số bằng nhau ta có:

\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\Rightarrow\frac{a^2}{b^2}=\left(\frac{a+c}{b+d}\right)^2\)(1)

\(\frac{a^2}{b^2}=\frac{a}{b}\cdot\frac{a}{b}=\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}\)(2)

từ (1) và (2) => đpcm