#1250 · Algebra · Quadratics

Bounds for variables in a quadratic relation

If $x$ and $y$ are two real quantities connected by the equation $9 x^{2} + 2 x y + y^{2} - 92 x - 20 y + 244 = 0$ , then will $x$ lie between 3 and 6, and $y$ between 1 and 10.

~12 minProof · checked by AIquadratic equationsdiscriminantreal bounds

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.c, No. 9

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