Question

Cho x > 0, y > 0. Biết x/2 = y/3 và x²y² = 576. Khi đó x - y =

Answer 1

Ta có:

\(\frac{x}{2}=\frac{y}{3}\)

\(\Leftrightarrow3x=2y\)

\(\Leftrightarrow y=1,5x\left(1\right)\)

Do \(x^2.y^2=576\)

\(\Leftrightarrow x.y=\sqrt{576}=24\left(2\right)\)

Thay \(\left(1\right)\) và \(\left(2\right)\)

\(\Leftrightarrow x.1,5x=24\)

\(\Leftrightarrow x^2=\frac{24}{1,5}=16\)

\(\Leftrightarrow x^2=16\Leftrightarrow x=\sqrt{16}=4\)

\(\Leftrightarrow y=1,5.4=6\)

\(\Leftrightarrow x-y=4-6=-2\)

Vậy \(x-y=-2\)