Question

3, a, Cho \(\dfrac{2x-y}{3x+2y}=\dfrac{5}{2}\) . Tính P= \(\dfrac{5x+4y}{25x-y}\)

b, Cho \(\dfrac{x-5y}{x-3y}=\dfrac{4}{3}\) . Tính P= \(\dfrac{x^3+2y^3}{x^3-y^3}\)

Answer 1

a: \(\dfrac{2x-y}{3x+2y}=\dfrac{5}{2}\)

\(\Leftrightarrow15x+10y=4x-2y\)

=>11x=-12y

=>\(\dfrac{x}{-12}=\dfrac{y}{11}\)

Đặt \(\dfrac{x}{-12}=\dfrac{y}{11}=k\)

=>x=-12k; y=11k

\(P=\dfrac{5x+4y}{25x-y}=\dfrac{5\cdot\left(-12k\right)+4\cdot11k}{25\cdot\left(-12k\right)-11k}=\dfrac{16}{311}\)

b: \(\dfrac{x-5y}{x-3y}=\dfrac{4}{3}\)

=>4x-12y=3x-15y

=>x=-3y

\(\Leftrightarrow\dfrac{x}{-3}=\dfrac{y}{1}=k\)

=>x=-3k; y=k

\(P=\dfrac{x^3+2y^3}{x^3-y^3}=\dfrac{-27k^3+2k^3}{-27k^3-k^3}=\dfrac{-25}{-28}=\dfrac{25}{28}\)