153.
\(\Leftrightarrow a^6+3a^4b^2+3a^2b^4+b^5=a^6+2a^3b^3+b^6\)
\(\Leftrightarrow3a^2b^2\left(a^2+b^2\right)=2a^3b^3\)
\(\Leftrightarrow\dfrac{a^2+b^2}{ab}=\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{a}{b}+\dfrac{b}{2}=\dfrac{2}{3}\)
154.
\(\dfrac{n^2+2n+1}{n+23}=\dfrac{\left(n-21\right)\left(n+23\right)+484}{n+23}=n-21+\dfrac{484}{n+23}\)
\(\Rightarrow n+23=Ư\left(484\right)\)
Mà n lớn nhất \(\Rightarrow n+23=484\)
\(\Rightarrow n=461\)
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