Question

1.Cho a/b=c/d chứng minh rằng:

a. c/b.d=a²+c²/b²+d².

b [a-b/c-d]⁴=a⁴+b⁴/c⁴+d⁴.

GIÚP MIK VỚI CÁC BẠN ƠI AI RA ĐÁP ÁN NHANH NHẤT MIK LIKE CHO.

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

a: \(\dfrac{ac}{bd}=\dfrac{bk\cdot dk}{bd}=k^2\)

\(\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{b^2k^2+d^2k^2}{b^2+d^2}=k^2\)

Do đó: \(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\)

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

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

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