#1903 · Algebra · Systems

Real Triads of Solutions

Shew that if $a$ , $b$ , $c$ are positive and unequal, the equations $a x + y + z = 0$ , $x + b y + z = 0$ , $x + y + cz = 0$ give three distinct triads of real values for $x$ , $y$ , $z$ ; and the ratio of the products of the three values of $x$ and $y$ is $b (b - c) : a (c - a)$ .

~30 minProof · checked by AIlinear systemsdeterminantsreal roots

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 298

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