Question

Answer 1

 

a: Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}=\dfrac{\left(bk+b\right)^3}{\left(dk+d\right)^3}=\dfrac{b^3}{d^3}\)

\(\dfrac{a^3+b^3}{c^3+đ^3}=\dfrac{b^3k^3+b^3}{d^3k^3+d^3}=\dfrac{b^3}{d^3}\)

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

b: \(\dfrac{4a^4+5b^4}{4c^4+5d^4}=\dfrac{4b^4k^4+5b^4}{4d^4k^4+5d^4}=\dfrac{b^4}{d^4}\)

\(\dfrac{a^2b^2}{c^2d^2}=\dfrac{b^2k^2\cdot b^2}{d^2\cdot k^2\cdot d^2}=\dfrac{b^4}{d^4}\)

=>\(\dfrac{4a^4+5b^4}{4c^4+5d^4}=\dfrac{a^2b^2}{c^2d^2}\)