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The pieces can be rotated and reflected. However, they cannot overlap ...

The function \(f(x)=x^4+ax^3+bx^2+cx+d\) has four positive roots. We are also given that \((b-a)(a+b)+(d-c)(c+d)=2(ac-bd).\)

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Given

\[\begin{cases}a,b,c,d>0\\ab+bc+cd+da=1,\end{cases}\]

\(k\) is the largest number such that

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The integer solutions to \[\displaystyle x^2+xy+y^2=x^2y^2\] are ordered pairs \(\displaystyle (x_1,y_1), (x_2,y_2),\ldots,(x_n,y_n)\).

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