- #1

MountEvariste

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Let $E$ be the set of all real $4$-tuples $(a, b, c, d)$ such that if $x, y \in \mathbb{ R}$, then:

$(ax+by)^2+(cx+dy)^2 \le x^2+y^2$.

Find the volume of $E$ in $\mathbb{R}^4$.

$(ax+by)^2+(cx+dy)^2 \le x^2+y^2$.

Find the volume of $E$ in $\mathbb{R}^4$.

*Source: AMM*.