Question

cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\)

1/ CM: \(\dfrac{5a+3b}{5a-3b}\)=\(\dfrac{5c+3d}{5c-3d}\)

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

3/CM: \(\dfrac{ab}{cd}\)=\(\dfrac{a^2+c^2}{b^2+d^2}\)

HELP ME

Answer 1

1.\(\dfrac{5a+3b}{5a-3b}\)=\(\dfrac{5c+3d}{5c-3d}\)

Ta có:\(\dfrac{a}{b}=\dfrac{c}{d}\)

=>\(\dfrac{a}{c}=\dfrac{b}{d}\)

=>\(\dfrac{5a}{5c}=\dfrac{3b}{3d}\)

=>\(\dfrac{5a+3b}{5c+3d}\)=\(\dfrac{5a-3b}{5c-3d}\)(a/d t/c của dãy tỉ số bằng nhau)

=>\(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)(đpcm)

Answer 2

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

Làm như câu trên tới đoạn:

\(\dfrac{7a^2+3b^2}{7c^2+7d^2}=\)\(\dfrac{11a^2-8b^2}{11c^2-8d^2}\)

=>\(\dfrac{7a^2+3ab}{7c^2+3cd}=\dfrac{11a^2-8b^2}{11c^2-8d^2}\)=>đề bài(đpcm)

3.Gải tương tự