Ta có: \(\left(\dfrac{x}{a}+\dfrac{y}{b}\right)=1\)
\(\Leftrightarrow\left(\dfrac{x}{a}+\dfrac{y}{b}\right)^2=1\)
\(\Leftrightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+2\cdot\dfrac{xy}{ab}=1\)
\(\Leftrightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=5\)
Ta có: \(\dfrac{x^3}{a^3}+\dfrac{y^3}{b^3}=\left(\dfrac{x}{a}\right)^3+\left(\dfrac{y}{b}\right)^3\)
\(=\left(\dfrac{x}{a}+\dfrac{y}{b}\right)\left(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}-\dfrac{xy}{ab}\right)\)
\(=1\cdot\left(5+2\right)=7\)
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