Question

1.C/m rằng

Nếu \(\dfrac{a}{b}=\dfrac{a}{c}\) thì

a,\(\dfrac{2a-3b}{2a+3b}=\dfrac{2c-3d}{3c+3d}\)

b,\(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\)

c,\(\left(\dfrac{a-b}{c-d}\right)^4=\dfrac{a^4+b^4}{c^4+d^4}\)

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

a: \(\dfrac{2a-3b}{2a+3b}=\dfrac{2bk-3b}{2bk+3b}=\dfrac{2k-3}{2k+3}\)

\(\dfrac{2c-3d}{2c+3d}=\dfrac{2dk-3d}{2dk+3d}=\dfrac{2k-3}{2k+3}\)

=>\(\dfrac{2a-3b}{2a+3b}=\dfrac{2c-3d}{2c+3d}\)

b: \(\dfrac{a+c}{b+d}=\dfrac{bk+dk}{b+d}=k\)

\(\dfrac{a-c}{b-d}=\dfrac{bk-dk}{b-d}=k\)

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

c: \(\left(\dfrac{a-b}{c-d}\right)^4=\left(\dfrac{bk-b}{dk-d}\right)^4=\left(\dfrac{b}{d}\right)^4\)

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

Do đó: \(\left(\dfrac{a-b}{c-d}\right)^4=\dfrac{a^4+b^4}{c^4+d^4}\)